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Volume 102

Number 4

Winter 2016

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Journal of the

WASHINGTON ACADEMY OF SCIENCES

Volume 102 Number4 Winter 2016

Contents

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Bose Einstein Condensation in a Dilute Gas E. Cornell & C. Wiemann ...........0000+- 53

Deinine and Measuring Optical Frequencies: J. Gall. cit.cs2...zeiecsecevsts ses nacatonceressee 101

Superposition, Entanglement, and Raising Schrédinger’s Cat D. Wineland .......... 14]

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ISSN 0043-0439 Issued Quarterly at Washington DC

Winter 2016

Editorial Remarks

This issue of the Journal is a special one. We dedicate this Journal to

Katharine Gebbie, who for over twenty years, directed the National Institute

of Standards and Technology’s (NIST) Physical Laboratory and its

successor, the Physical Measurement Laboratory (PML).

Over decades of service Gebbie accumulated an impressive list of honors

recognizing her work and impact. They include two Department of

Commerce (DoC) Gold Medals, a DoC Distinguished Rank Award, the

NIST Equal Employment Opportunity award, a Lifetime Achievement

Award from the professional society Women in Science and Engineering,

the Washington Academy of Science’s Physical Science Award, a special

award from the American Physical Society for her leadership role in

fostering excellence in Atomic, Molecular, and Optical science, and the

2002 Service to America Award from the Partnership for Public Service —

the first of such recognitions given to anyone at NIST. She is also a Fellow

of the Washington Academy of Sciences, the American Association of Arts

and Sciences, the American Academy of Arts and Sciences, and the

American Physical Society. She was Vice-President of the International

Committee on Weights and Measures (CIPM) from 1993 to1999.

She was named after her aunt, Katharine Burr Blodgett, who was the first

woman to earn a Ph.D. in physics from the University of Cambridge, a

world-class scientist, a long-time colleague of Irving Langmuir at General

Electric, and the co-discoverer of Langmuir-Blodgett thin films.

She was married to Alastair Gebbie, a pioneer in Fourier Transform

Spectroscopy.

She was known for her kindness and wisdom. I came to know her late and

saw that unique person who shone with excitement for science and for the

people who work in it. It was a singular privilege to have known her. She

strongly supported the Washington Academy of Science’s awards program.

We could always depend on her to submit superb candidates for awards.

In arare move Gebbie’s colleagues renamed NIST’s precision measurement

laboratory in Boulder, Colorado in her honor. “This renaming is our small

way of saying thank you... for all [Katharine] has done for this organization

over such a long period of time,” said NIST Director Willie E. May.

An astrophysicist by training, Gebbie received her B.A. in Physics from

Bryn Mawr College, subsequently earning a B.S. in Astronomy and Ph.D.

in Physics from University College London.

Washington Academy of Sciences

111

For several years in the mid-1960s she trekked in Nepal, went

mountaineering in Turkey, and flew around North America in her mother’s

airplane. Both Dr. Gebbie and her parents had taken professional flying

lessons.

Please enjoy this issue in honor of Katharine Gebbie.

Sethanne Howard

Editor

Winter 2016

A Tribute to Katharine Blodgett Gebbie

KATHARINE BLODGETT GEBBIE, a Fellow of the Washington Academy of

Sciences, was born on 4 July 1932 and died on 17 August 2016. Katharine

spent most of her professional career at the

National Institute of Standards and

Technology (originally the National Bureau

of Standards). Trained as an astrophysicist,

she began her association with NBS/NIST

in 1966 as a postdoc at JILA, then known as

the Joint Institute for Laboratory

Astrophysics, a cooperative operation of

NIST and the University of Colorado at

Boulder. After a distinguished career in

research, Katharine was persuaded to turn

her talents to scientific management. A

series of increasingly responsible positions

led her to become the founding Director of

NIST’s Physics Laboratory in 1991. She remained the director of that

Laboratory for all of its 20 years and was also the founding director of its

even larger successor, the NIST Physical Measurement Laboratory. Many

of us believe her laboratory to be the best place in the entire world in which

to do research in Physics, predominantly because of the atmosphere that

Katharine created. Her creed was to hire the best people, give them the

resources to do their work, and let them do it. While many other managers

might have said similar things, she actually did it, and the results were

astounding. Within a span of 15 years, four of her scientists received Nobel

Prizes in Physics. Two of her researchers received the prestigious

MacArthur awards, and many other accolades were bestowed on those

under her leadership. She was a true servant, and gloried in the

accomplishments of those she nurtured.

This issue of the Journal of the Washington Academy of Sciences pays

tribute to Katharine Blodgett Gebbie by reprinting the “Nobel Lectures” of

Katharine’s four Laureates, William Phillips (1997), Eric Cornell (2001),

John Hall (2005), and David Wineland (2012). These are the articles

prepared by the Laureates for publication in Reviews of Modern Physics a

few months after the award of the Nobel Prize, and are not transcripts of the

Washington Academy of Sciences

Nobel Lectures delivered in Stockholm during the events association with

the 10 December prize award ceremony. The article by Cornell is co-

authored with his University of Colorado colleague Carl Wieman, with

whom he worked closely at JILA, and who also benefitted from Katharine

Gebbie’s leadership.

William D. Phillips

Gaithersburg

January 2017

Winter 2016

Journal of the Washington Academy of Sciences

Editor Sethanne Howard sethanneh@msn.com

Board of Discipline Editors

The Journal of the Washington Academy of Sciences has an 11-member

Board of Discipline Editors representing many scientific and technical

fields. The members of the Board of Discipline Editors are affiliated with a

variety of scientific institutions in the Washington area and beyond —

government agencies such as the National Institute of Standards and

Technology (NIST); universities such as Georgetown; and professional

associations such as the Institute of Electrical and Electronics Engineers

WEEE).

Anthropology Emanuela Appetiti eappetiti@hotmail.com

Astronomy Sethanne Howard sethanneh@msn.com

Biology/Biophysics Eugenie Mielczarek mielcezar@physics.gmu.edu

Botany Mark Holland maholland@salisbury.edu

Chemistry Deana Jaber djaber@marymount.edu

Environmental Natural

Sciences Terrell Erickson terrell.ericksonl @wde.nsda.gov

Health - Robin Stombler rstombler@auburnstrat.com

History of Medicine Alain Touwaide atouwaide@hotmail.com

Operations Research Michael Katehakis mnk(@rci.rutgers.edu

Science Education Jim Egenrieder jim@deepwater.org

Systems Science Elizabeth Corona elizabethcorona@gmail.com

Washington Academy of Sciences

Laser cooling and trapping of neutral atoms’

William D. Phillips

National Institute of Standards and Technology,

Introduction

IN 1978, WHILE I WAS A POSTDOCTORAL fellow at MIT, I read a

paper by Art Ashkin (1978) in which he described how one might

slow down an atomic beam of sodium using the radiation pressure of

a laser beam tuned to an atomic resonance. After being slowed, the

atoms would be captured in a trap consisting of focused laser beams,

with the atomic motion being damped until the temperature of the

atoms reached the microkelvin range. That paper was my first

introduction to laser cooling, although the idea of laser cooling (the

reduction of random thermal velocities using radiative forces) had been

proposed three years earlier in independent papers by Hansch and

Schawlow (1975) and Wineland and Dehmelt (1975). Although the

treatment in Ashkin’s paper was necessarily over-simplified, it

provided one of the important inspirations for what I tried to

accomplish for about the next decade. Another inspiration appeared

later that same year: Wineland, Drullinger and Walls (1978) published

the first laser cooling experiment, in which they cooled a cloud of

Mg’ ions held in a Penning trap. At essentially the same time,

Neuhauser, Hohenstatt, Toschek and Dehmelt (1978) also reported

laser cooling of trapped Ba’ ions.

Those laser cooling experiments of 1978 were a dramatic

demonstration of the mechanical effects of light, but such effects have a

much longer history. The understanding that electromagnetic radiation

exerts a force became quantitative only with Maxwell’s theory of

electromagnetism, even though such a force had been conjectured much

earlier, partly in response to the observation that comet tails point away

from the sun. It was not until the turn of the century, however, that

experiments by Lebedev (1901) and Nichols and Hull (1901, 1903) gave

| The 1997 Nobel Prize in Physics was shared by Steven Chu, Claude N. Cohen-Tannoudji,

and William D. Phillips. This text is based on Dr. Phillips’s address on the occasion of the

award. Reprinted from Reviews of Modern Physics, Vol. 70, No. 3, July 1998.

Winter 2016

a laboratory demonstration and quantitative measurement of radiation

pressure on macroscopic objects. In 1933 Frisch made the first

demonstration of light pressure on atoms, deflecting an atomic sodium

beam with resonance radiation from a lamp. With the advent of the laser,

Ashkin (1970) recognized the potential of intense, narrow-band light for

manipulating atoms and in 1972 the first “modern” experiments

demonstrated the deflection of atomic beams with lasers (Picqué and

Vialle, 1972; Schieder et al., 1972). All of this set the stage for the laser

cooling proposals of 1975 and for the demonstrations in 1978 with ions.

Comet tails, deflection of atomic beams and the laser cooling

proposed in 1975 are all manifestations of the radiative force that Ashkin

has called the “scattering force,” because it results when light strikes an

object and is scattered in random directions. Another radiative force, the

dipole force, can be thought of as arising from the interaction between

an induced dipole moment and the gradient of the incident light field.

The dipole force was recognized at least as early as 1962 by Askar’ yan,

and in 1968, Letokhov proposed using it to trap atoms — even before

the idea of laser cooling! The trap proposed by Ashkin in 1978 relied on

this “dipole” or “gradient” force as well. Nevertheless, in 1978, laser

cooling, the reduction of random velocities, was understood to involve

only the scattering force. Laser trapping, confinement in a potential

created by light, which was still only a dream, involved both dipole and

scattering forces. Within 10 years, however, the dipole force was seen

to have a major impact on laser cooling as well.

Without understanding very much about what difficulties lay in

store for me, or even appreciating the exciting possibilities of what one

might do with laser cooled atoms, I decided to try to do for neutral atoms

what the groups in Boulder and Heidelberg had done for ions: trap them

and cool them. There was, however, a significant difficulty: we could

not first trap and then cool neutral atoms. lon traps were deep enough to

easily trap ions having temperatures well above room temperature, but

none of the proposed neutral atom traps had depths of more than a few

kelvin. Significant cooling was required before trapping would be

possible, as Ashkin had outlined in his paper (1978), and it was with this

idea that I began.

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o>)

Before describing the first experiments on the deceleration of

atomic beams, let me digress slightly and discuss why laser cooling is

so exciting and why it has attracted so much attention in the scientific

community: When one studies atoms in a gas, they are typically moving

very rapidly. The molecules and atoms in air at room temperature are

moving with speeds on the order of 300 m/s, the speed of sound. This

thermal velocity can be reduced by refrigerating the gas, with the

velocity varying as the square root of the temperature, but even at 77 K,

the temperature at which N2 condenses into a liquid, the nitrogen

molecules are moving at about 150 m/s. At 4 K, the condensation

temperature of helium, the He atoms have 90 m/s speeds. At

temperatures for which atomic thermal velocities would be below | m/s,

any gas in equilibrium (other than spin-polarized atomic hydrogen)

would be condensed, with a vapor pressure so low that essentially no

atoms would be in the gas phase. As a result, all studies of free atoms

were done with fast atoms. The high speed of the atoms makes

measurements difficult. The Doppler shift and the relativistic time

dilation cause displacement and broadening of the spectral lines of

thermal atoms, which have a wide spread of velocities. Furthermore, the

high atomic velocities limit the observation time (and thus the spectral

resolution) in any reasonably-sized apparatus. Atoms at 300 m/s pass

through a meter-long apparatus in just 3 ms. These effects are a major

limitation, for example, to the performance of conventional atomic

clocks.

The desire to reduce motional effects in spectroscopy and atomic

clocks was and remains a major motivation for the cooling of both

neutral atoms and ions. In addition, some remarkable new phenomena

appear when atoms are sufficiently cold. The wave, or quantum nature

of particles with momentum p becomes apparent only when the de

Broglie wavelength, given by Aas = h/p, becomes large, on the order of

relevant distance scales like the atom-atom interaction distances, atom-

atom separations, or the scale of confinement. Laser cooled atoms have

allowed studies of collisions and of quantum collective behavior in

regimes hitherto unattainable. Among the new phenomena seen with

neutral atoms is Bose-Einstein condensation of an atomic gas (Anderson

et al., 1995; Davis, Mewes, Andrews, eft al., 1995), which has been

hailed as a new state of matter, and is already becoming a major new

Winter 2016

field of investigation. Equally impressive and exciting are the quantum

phenomena seen with trapped ions, for example, quantum jumps

(Bergquist ef al., 1986; Nagourney ef al., 1986; Sauter et al., 1986),

Schrédinger cats (Monroe ef al., 1996), and quantum logic gates

(Monroe ef al., 1995).

Laser Cooling of Atomic Beams

In 1978 I had only vague notions about the excitement that lay

ahead with laser cooled atoms, but I concluded that slowing down an

atomic beam was the first step. The atomic beam was to be slowed using

the transfer of momentum that occurs when an atom absorbs a photon.

Figure 1 shows the basic process underlying the “scattering force” that

results. An atomic beam with velocity v is irradiated by an opposing

laser beam. For each photon that a ground-state atom absorbs, it is

slowed by vVree= h k/m. In order to absorb again the atom must return to

the ground state by emitting a photon. Photons are emitted in random

directions, but with a symmetric average distribution, so their

contribution to the atom’s momentum averages to zero. The randomness

results in a “heating” of the atom, discussed below.

FIG. 1. (a) An atom with velocity v encounters a photon with momentum

hk=h/X,; (b) after absorbing the photon, the atom is slowed by hk/m:; (c) after

re-radiation in a random direction, on average the atom is slower than in (a).

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For sodium atoms interacting with the familiar yellow resonance

light, vree = 3 cm/s, while a typical beam velocity is about 10° cm/s, so

the absorption-emission process must occur about 3 x 10* times to bring

the Na atom to rest. In principle, an atom could radiate and absorb

photons at half the radiative decay rate of the excited state (a 2-level

atom in steady state can spend at most half of its time in the excited

state). For Na, this implies that a photon could be radiated every 32

ns on average, bringing the atoms to rest in about 1 ms. Two

problems, optical pumping and Doppler shifts, can prevent this from

happening. I had an early indication of the difficulty of decelerating

an atomic beam shortly after reading Ashkin’s 1978 paper. I was

then working with a sodium atomic beam at MIT, using tunable

dye lasers to study the scattering properties of optically excited

sodium. I tuned a laser to be resonant with the Na transition from

3p1/2 —> 3P3/o, the D2 line, and directed its. beam opposite to the

atomic beam. I saw that the atoms near the beam source were

fluorescing brightly as they absorbed the laser light, while further

away from the source, the atoms were relatively dim. The problem,

I concluded, was optical pumping, illustrated in Fig. 2.

Sodium is not a two-level atom, but has two ground hyperfine

levels (F=1 and F=2 in Fig. 2), each of which consists of several,

normally degenerate, states. Laser excitation out of one of the

hyperfine levels to the excited state can result in the atom radiating

to the other hyperfine level. This optical pumping essentially shuts

off the absorption of laser light, because the linewidths of the

transition and of the laser are much smaller than the separation

between the ground state hyperfine components. Even for atoms

excited on the 3S1/2 (F=2) — 3P3/2 (F’ =3) transition, where the

only allowed decay channel is to -'=2, off-resonant excitation of

F’=2 (the linewidth of the transition is 10 MHz, while the

separation between /’=2 and F’=3 is 60 MHz) leads to optical

pumping into /=1 after only about a hundred absorptions. This

optical pumping made the atoms “dark” to my laser after they

traveled only a short distance from the source.

An obvious solution [Fig. 2(b)] is to use a second laser

frequency, called a repumper, to excite the atoms out of the “wrong”

Winter 2016

(F'=1) hyperfine state so that they can decay to the “right” state

(F'=2) where they can continue to cool. Given the repumper, another

problem becomes apparent: the Doppler shift. In order for the laser

light to be resonantly absorbed by a counter-propagating atom

moving with velocity v, the frequency @ of the light must be kv

lower than the resonant frequency for an atom at rest. As the atom

repeatedly absorbs photons, slowing down as desired, the Doppler

shift changes and the atom goes out of resonance with the light. The

natural linewidth I’/2n of the optical transition in Na is 10 MHz (full

width at half maximum). A change in velocity of 6 m/s gives a

Doppler shift this large, so after absorbing only 200 photons, the

atom is far enough off resonance that the rate of absorption is

significantly reduced. The result is that only atoms with the “proper”

velocity to be resonant with the laser are slowed, and they are only

slowed by a small amount.

z aaa 2

aaa es

1 0 8

a l b repumper

Fe F=2

| I

FIG. 2. (a) The optical pumping process preventing cycling transitions in

alkalis like Na; (b) use of a repumping laser to allow many absorption-emission

cycles.

Nevertheless, this process of atoms being slowed and pushed

out of resonance results in a cooling or narrowing of the velocity

distribution. In an atomic beam, there is typically a widespread of

velocities around vth = 3kp7/m. Those atoms with the proper

velocity will absorb rapidly and decelerate. Those that are too fast

will absorb more slowly, then more rapidly as they come into

resonance, and finally more slowly as they continue to decelerate.

Atoms that are too slow to begin with will absorb little and

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decelerate little. Thus atoms from a range of velocities around the

resonant velocity are pushed into a narrower range centered on a

lower velocity. This process was studied theoretically by Minogin

(1980) and in 1981, at Moscow’s Institute for Spectroscopy, was

used in the first experiment clearly demonstrating laser cooling of

neutral atoms (Andreev ef al., 1981).

Figure 3 shows the velocity distribution after such cooling

of an atomic beam. The data was taken in our laboratory, but is

equivalent to what had been done in Moscow. The characteristic of

this kind of beam cooling is that only a small part of the total velocity

distribution (the part near resonance with the laser beam) is slowed

by only a small amount (until the atoms are no longer resonant).

The narrow peak, while it represents true cooling in that its velocity

distribution 1s narrow, consists of rather fast atoms.

density of atoms (arb. units)

0 400 800 1200

velocity (m/s)

FIG. 3. Cooling an atomic beam with a fixed frequency laser. The dotted curve

is the velocity distribution before cooling, and the solid curve is after cooling.

Atoms from a narrow velocity range are transferred to a slightly narrower range

centered on a lower velocity.

Winter 2016

One solution to this problem had already been outlined in

1976 by Letokhov, Minogin, and Pavlik. They suggested a general

method of changing the frequency (chirping) of the cooling laser so

as to interact with all the atoms in a wide distribution and to stay 1n

resonance with the atoms as they are cooled. The Moscow group

applied the technique to decelerating an atomic beam (Balykin ef

al., 1979) but without clear success (Balykin, 1980). [Later, in 1983,

John Prodan and I obtained the first clear deceleration and cooling

of an atomic beam with this “chirp-cooling” technique (Phillips

and Prodan, 1983, 1984; Phillips, Prodan, and Metcalf, 1983a; Prodan

and Phillips, 1984). Those first attempts failed to bring the atoms to

rest, something that was finally achieved by Ertmer, Blatt, Hall and

Zhu (1985).] The chirp-cooling technique is now one of the two

standard methods for decelerating beams. The other is “Zeeman

cooling.”

By late 1978, I had moved to the National Bureau of

Standards (NBS), later named the National Institute of Standards

and Technology (NIST), in Gaithersburg. I was considering how to

slow an atomic beam, realizing that the optical pumping and

Doppler shift problems would both need to be addressed. I

understood how things would work using the Moscow chirp-cooling

technique and a repumper. I also considered using a broadband laser,

so that there would be light in resonance with the atoms, regardless

of their velocity. [This idea was refined by Hoffnagle (1988) and

demonstrated by Hall’s group (Zhu, Oates, and Hall, 1991).]

Finally I considered that instead of changing the frequency of the

laser to stay 1n resonance with the atoms (chirping), one could use a

magnetic field to change the energy level separation in the atoms

so as to keep them in resonance with the fixed-frequency laser

(Zeeman cooling). All of these ideas for cooling an atomic beam,

along with various schemes for avoiding optical pumping, were

contained in a proposal (Phillips, 1979) that I submitted to the Office

of Naval Research in 1979. Around this time Hal Metcalf, from the

State University of New York at Stony Brook, joined me in

Gaithersburg and we began to consider what would be the best way

to proceed. Hal contended that all the methods looked reasonable,

but we should work on the Zeeman cooler because it would be the

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most fun! Not only was Hal right about the fun we would have, but

his suggestion led us to develop a technique with particularly

advantageous properties. The idea is illustrated in Fig. 4.

taper

bias

atomic _ Cy zzz

SOU ee YUH) fy JVI Via

cooling laser

B(z)

FIG. 4. Upper: Schematic representation of a Zeeman slower. Lower: Variation

of the axial field with position.

The atomic beam source directs atoms, which have a wide

range of velocities, along the axis (z direction) of a tapered solenoid.

This magnet has more windings at its entrance end, near the source,

so the field is higher at that end. The laser is tuned so that, given the

field-induced Zeeman shift and the velocity-induced Doppler shift of

the atomic transition frequency, atoms with velocity vo are resonant

with the laser when they reach the point where the field is maximum.

Those atoms then absorb light and begin to slow down. As their

velocity changes, their Doppler shift changes, but 1s compensated by

the change in Zeeman shift as the atoms move to a point where the

field is weaker. At this point, atoms with initial velocities slightly

lower than vo come into resonance and begin to slow down. The

process continues with the initially fast atoms decelerating and

staying in resonance while initially slower atoms come into

resonance and begin to be slowed as they move further down the

solenoid. Eventually all the atoms with velocities lower than vo are

brought to a final velocity that depends on the details of the

magnetic field and laser tuning.

The first tapered solenoids that Hal Metcalf and I used for

Zeeman cooling of atomic beams had only a few sections of

Winter 2016

windings and had to be cooled with air blown by fans or with wet

towels wrapped around the coils. Shortly after our initial success

in getting some substantial deceleration, we were joined by my first

postdoc, John Prodan. We developed more sophisticated solenoids,

wound with wires in many layers of different lengths, so as to

produce a smoothly varying field that would allow the atoms to

slow down to a stop while remaining in resonance with the cooling

laser.

These later solenoids were cooled with water flowing over the

coils. To improve the heat transfer, we filled the spaces between the

wires with various heat-conducting substances. One was a white

silicone grease that we put onto the wires with our hands as we

wound the coil on a lathe. The grease was about the same color and

consistency as the diaper rash ointment I was then using on my baby

daughters, so there was a period of time when, whether at home

or at work, I seemed to be up to my elbows in white grease.

The grease-covered, water-cooled solenoids had _ the

annoying habit of burning out as electrolytic action attacked the

wires during operation. Sometimes it seemed that we no sooner

obtained some data than the solenoid would burn out and we were

winding a new one.

On the bright side, the frequent burn-outs provided the

opportunity for refinement and redesign. Soon we were

embedding the coils in a black, rubbery resin. While it was

supposed to be impervious to water, it did not have good adhesion

properties (except to clothing and human flesh) and the solenoids

continued to burn out. Eventually, an epoxy coating sealed the

solenoid against the water that allowed the electrolysis, and in

more recent times we replaced water with a fluorocarbon liquid

that does not conduct electricity or support electrolysis. Along the

way to a reliable solenoid, we learned how to slow and stop atoms

efficiently (Phillips and Metcalf, 1982; Prodan, Phillips, and

Metcalf, 1982; Phillips, Prodan, and Metcalf, 1983a, 1983b,

1984a, 1984b, 1985; Metcalfand Phillips, 1985).

The velocity distribution after deceleration is measured in

a detection region some distance from the exit end of the solenoid.

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Here a separate detection laser beam produces fluorescence from

atoms having the correct velocity to be resonant. By scanning the

frequency of the detection laser, we were able to determine the

velocity distribution in the atomic beam. Observations with the

detection laser were made just after turning off the cooling laser, so

as to avoid any difficulties with having both lasers on at the same

time. Figure 5 shows the velocity distribution resulting from

Zeeman cooling: a large fraction of the initial distribution has been

swept down into a narrow final velocity group.

One of the advantages of the Zeeman cooling technique is

the ease with which the optical pumping problem is avoided. Because

the atoms are always in a strong axial magnetic field (that is the

reason for the “bias” windings in Fig. 4), there is a well-defined axis

of quantization that allowed us to make use of the selection rules for

radiative transitions and to avoid the undesirable optical pumping.

Figure 6 shows the energy levels of Na in a magnetic field. Atoms

in the 31/2 (mr=2) state, irradiated with circularly polarized o*

light, must increase their mr by one unit, and so can go only to the

3P3/2 (mr =3) state. This state in turn can decay only to 3S1/2 (mr

=2), and the excitation process can be repeated indefinitely. Of

course, the circular polarization is not perfect, so other excitations

are possible, and these may lead to decay to other states. Fortunately,

in a high magnetic field, such transitions are highly unlikely (Phillips

and Metcalf, 1982): either they involve a change in the nuclear spin

projection m,, which is forbidden in the high field limit, or they are

far from resonance. These features, combined with high purity of the

circular polarization, allowed us to achieve, without a “wrong

transition,” the 3 x 10% excitations required to stop the atoms.

Furthermore, the circular polarization produced some “good” optical

pumping: atoms not initially in the 31/2 (mr=2) state were pumped

into this state, the “stretched” state of maximum projection of

angular momentum, as they absorbed the angular momentum of the

light. These various aspects of optical selection rules and optical

pumping allowed the process of Zeeman cooling to be very efficient,

decelerating a large fraction of the atoms in the beam.

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density of atoms (arb. units)

tt) 400 800 1200 1400 1600 1800

velocity (m/s)

FIG. 5. Velocity distribution before (dashed) and after (solid) Zeeman cooling.

The arrow indicates the highest velocity resonant with the slowing laser. (The extra

bump at 1700 m/s is from F'=1 atoms, which are optically pumped into F=2

during the cooling process.)

orNnw 8

AorN

Rot D®

Magnetic Field

FIG. 6. Energy levels of Na in a magnetic field. The cycling transition used for

laser cooling is shown as a solid arrow, and one of the nearly forbidden excitation

channels leading to undesirable optical pumping is shown dashed.

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In 1983 we discussed a number of these aspects of laser

deceleration, including our early chirp-cooling results, at a two-day

workshop on “Laser-Cooled and Trapped Atoms” held at NBS in

Gaithersburg (Phillips, 1983). I view this as an important meeting in

that it and its proceedings stimulated interest in laser cooling. In

early 1984, Stig Stenholm, then of the University of Helsinki,

organized an international meeting on laser cooling in Tvérminne, a

remote peninsula in Finland. Figure 7 shows the small group

attending (I was the photographer), and in that group, only some of

the participants were even active in laser cooling at the time.

Among these were Stig Stenholm [who had done pioneering work

in the theory of laser cooling and the mechanical effects of light on

atoms (Stenholm, 1978a, 1978b, 1985, 1986; Javanainen and

Stenholm, 1980a, 1980b, 1980c, 1981a, 1981b)] along with some of

his young colleagues; Victor Balykin and Vladimir Minogin from the

Moscow group; and Claude Cohen-Tannoudji and Jean Dalibard

from Ecole Normale Supérieure (ENS) in Paris, who had begun

working on the theory of laser cooling and trapping. Also present

were Jiirgen Mlynek and Wolfgang Ertmer, both of whom now

lead major research groups pursuing laser cooling and atom optics.

At that time, however, only our group and the Moscow group had

published any experiments on cooling of neutral atoms.

Much of the discussion at the Tvaérminne meeting involved

the techniques of beam deceleration and the problems with optical

pumping. I took a light-hearted attitude toward our trials and

tribulations with optical pumping, often joking that any unexplained

features in our data could certainly be attributed to optical pumping.

Of course, at the Ecole Normale, optical pumping had a long and

distinguished history. Having been pioneered by Alfred Kastler and

Jean Brossel, optical pumping had been the backbone of many

experiments in the Laboratoire de Spectroscopie Hertzienne (now

the Laboratoire Kastler Brossel). After one discussion in which I

had joked about optical pumping, Jean Dalibard privately mentioned

to me, “You know, Bill, at the Ecole Normale, optical pumping is

not a joke.” His gentle note of caution calmed me down a bit,

but it turned out to be strangely prophetic as well. As we saw a few

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years later, optical pumping had an important, beautiful, and totally

unanticipated role to play in laser cooling, and it was surely no joke.

FIG. 7. Stig Stenholm’s “First International Conference on Laser Cooling” in

Tvarminne, March 1984. Back row, left to right: Juha Javanainen, Markus

Lindberg, Stig Stenholm, Matti Kaivola, Nis Bjerre, (unidentified), Erling

Rus, Rainer Salomaa, Vladimir Minogin. Front row: Jirgen Mlynek, Angela

Guzmann, Peter Jungner, Wolfgang Ertmer, Birger Stahlberg, Olli Serimaa, Jean

Dalibard, Claude Cohen-Tannoudji, Victor Balykin.

Stopping Atoms

As successful as Zeeman cooling had been in producing large

numbers of decelerated atoms as in Fig. 5, we had not actually

observed the atoms at rest, nor had we trapped them. In fact, I recall

a conversation with Steve Chu that took place during the

International Conference on Laser Spectroscopy in Interlaken in

1983 in which I had presented our results on beam deceleration

(Phillips, Prodan, and Metcalf, 1983a). Steve was working on

positronium spectroscopy but was wondering whether there still

might be something interesting to be done with laser cooling of

neutral atoms. I offered the opinion that there was still plenty to do,

and in particular, that trapping of atoms was still an unrealized goal.

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It wasn’t long before each of us achieved that goal, in very different

ways.

Our approach was first to get some stopped atoms. The

problem had been that, in a sense, Zeeman cooling worked too well.

By adjusting the laser frequency and magnetic field, we could, up to

a point, choose the final velocity of the atoms that had undergone

laser deceleration. Unfortunately, if we chose too small a velocity, no

slow atoms at all appeared in the detection region. Once brought

below a certain velocity, about 200 m/s, the atoms always continued

to absorb enough light while traveling from the solenoid to the

detection region so as to stop before reaching the detector. By

shutting off the cooling laser beam and delaying observation until

the slow atoms arrived in the observation region, we were able to

detect atoms as slow as 40 m/s with a spread of 10 m/s,

corresponding to a temperature (in the atoms’ rest frame) of 70 mK

(Prodan, Phillips, and Metcalf, 1982).

The next step was to get these atoms to come to rest in our

observation region. We were joined by Alan Migdall, a new

postdoc, Jean Dalibard, who was visiting from ENS, and Ivan So, Hal

Metcalf’s student. We decided that we needed to proceed as before,

shutting off the cooling light, allowing the slow atoms to drift into

the observation region, but then to apply a short pulse of additional

cooling light to bring the atoms to rest. The sequence of laser pulses

required to do this —a long pulse of several milliseconds for doing

the initial deceleration, followed by a delay and then another pulse

of a few hundred microseconds, followed by another delay before

detection — was provided by a rotating wheel with a series of

openings corresponding to the places where the laser was to be on.

Today we accomplish such pulse sequences with acousto-optic

modulators under computer control, but in those days it required

careful construction and balancing of a rapidly rotating wheel.

The result of this sequence of laser pulses was that we had

atoms at rest in our observation region with a velocity spread

corresponding to <100 mK (Prodan ef al., 1985). Just following

our 1985 paper reporting this in Physical Review Letters was a

report of the successful stopping of atoms by the chirp-cooling

Winter 2016

method in Jan Hall’s group (Ertmer, Blatt, Hall, and Zhu, 1985).

At last there were atoms slow enough to be trapped, and we decided

to concentrate first on magnetostatic trapping.

Magnetic Trapping of Atoms

The idea for magnetic traps had first appeared in the literature

as early as 1960 (Heer, 1960, 1963; Vladimirskii, 1960), although

Wolfgang Paul had discussed them in lectures at the University of

Bonn in the mid-1950s, as a natural extension of ideas about

magnetic focusing of atomic beams (Vauthier, 1949; Friedburg,

1951; Friedburg and Paul, 1951). Magnetic trapping had come to our

attention particularly because of the successful trapping of cold

neutrons (Kugler ef a/l., 1978). We later learned that in unpublished

experiments in Paul’s laboratory, there were indications of confining

sodium in a magnetic trap (Martin, 1975).

The idea of magnetic trapping is that in a magnetic field, an

atom with a magnetic moment will have quantum states whose

magnetic or Zeeman energy increases with increasing field and states

whose energy decreases, depending on the orientation of the moment

compared to the field. The increasing-energy states, or low-field-

seekers, can be trapped in a magnetic field configuration having a

point where the magnitude of the field is a relative minimum. [No de

field can have a relative maximum in free space (Wing, 1984), so

high-field-seekers cannot be trapped.] The requirement for stable

trapping, besides the kinetic energy of the atom being low enough, is

that the magnetic moment move adiabatically in the field. That is, the

orientation of the magnetic moment with respect to the field should

not change.

We considered some of the published designs for trapping

neutrons, including the spherical hexapole (Golub and Pendlebury,

1979), a design comprising three current loops, but we found them

less than ideal. Instead we decided upon a simpler design, with two

loops, which we called a spherical quadrupole. The trap, its magnetic

field lines and equipotentials are shown in Fig. 8. Although we

thought that we had discovered an original trap design, we later

learned that Wolfgang Paul had considered this many years ago, but

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had not given it much attention because atoms were not harmonically

bound in such a trap. In fact, the potential for such a trap is linear in

the displacement from the center and has a cusp there.

With a team consisting of Alan Migdall, John Prodan, Hal

Metcalf and myself, and with the theoretical support of Tom

Bergeman, we succeeded in trapping atoms in the apparatus shown

in Fig. 9 (Migdall ef al., 1985). As in the experiments that stopped

atoms, we start with Zeeman slowing, decelerating the atoms to 100

m/s in the solenoid. The slowing laser beam is then extinguished,

allowing the atoms to proceed unhindered for 4 ms to the magnetic

trap. At this point, only one of the two trap coils has current; it

produces a magnetic field that brings the atoms into resonance with

the cooling laser when it is turned on again for 400 us, bringing the

atoms to rest. Once the atoms are stopped, the other coil 1s energized,

producing the field shown in Fig. 8, and the trap is sprung. The atoms

are held in the trap until released, or until collisions with the room-

temperature background gas molecules in the imperfect vacuum

knock them out. After the desired trapping time, we turn off the

magnetic field, and turn on a probe laser, so as to see how many

atoms remain in the trap. By varying the frequency of this probe on

successive repetitions of the process, we could determine the velocity

distribution of the atoms, via their Doppler shifts.

The’ depth “of “our “trap was “about, 17 mK (25 md);

corresponding to Na atoms with a velocity of 3.5 m/s. In the absence

of trapping fields, atoms that fast would escape from the region of

the trap coils in a few milliseconds. Figure 10 shows a section of

chart paper with spectra of the atoms remaining after 35 ms of

trapping time. If the trap had not been working, we would have seen

essentially nothing after that length of time, but the signal, noisy as

it was, was unmistakable. It went away when the trap was off, and it

went away when we did not provide the second pulse of cooling light

that stops the atoms before trapping them. This was just the signature

we were looking for, and Hal Metcalf expressed his characteristic

elation at good results with his exuberant *“*WAHOO!!”’ at the top of

the chart.

Winter 2016

upstream coil downstream coil

R(cm)

Z(cm)

FIG. 8. (a) Spherical quadrupole trap with lines of B-field. (b) Equipotentials of

our trap (equal field magnitudes in millitesla), in a plane containing the

symmetry (Zz) axis.

As the evening went on, we were able to improve the signal,

but we found that the atoms did not stay very long in the trap, a

feature we found a bit frustrating. Finally, late in the evening we

decided to go out and get some fast food, talk about what was

happening and attack the problem afresh. When we returned a little

later that night, the signal had improved and we were able to trap

atoms for much longer times. We soon realized that during our

supper break the magnetic trap had cooled down, and stopped

outgassing, so the vacuum just in the vicinity of the trap improved

considerably. With this insight we knew to let the magnet cool off

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from time to time, and we were able to take a lot of useful data. We

continued taking data until around 5:00 am, and it was probably close

to 6:00 am when my wife Jane found Hal and me in our kitchen,

eating ice cream as she prepared to leave for work. Her dismay at the

lateness of our return and our choice of nourishment at that hour was

partially assuaged by Hal’s assurance that we had accomplished

something pretty important that night.

COLLECTION ee

ee BEAM MECHANICAL

SHUTTERS

Na BEAM BEAM

EXPANDER

COOLING

LASER BEAM

MECHANICAL TAPERED UPSTREAM DOWNSTREAM NEARLY MERGED

SHUTTER SOLENOID COIL COIL LASER BEAMS MECHANICAL

CHOPPER

—— ed

TRAP

FIG. 9. Schematic of the apparatus used to trap atoms magnetically.

Figure 11(a) presents the sequence of spectra taken after

various trapping times, showing the decrease in signal as atoms are

knocked out of the trap by collisions with the background gas

molecules. Figure 11(b) shows that the loss of atoms from the trap

is exponential, as expected, with a lifetime of a bit less than one

second, in a vacuum of a few times 10° pascals. A point taken

when the vacuum was allowed to get worse ilustrates that poor

vacuum made the signal decay faster. In more recent times, we and

others have achieved much longer trapping times, mainly because of

an improved vacuum. We now observe magnetic trap lifetimes of

one minute or longer in our laboratory.

Winter 2016

FIG. 10. A section of chart paper from 15 March 1985. “PC” and “no PC” refer

to presence or absence of the “‘post-cooling’’ pulse that brings the atoms to

rest in the trapping region.

Since our demonstration (Migdall et al., 1985) of magnetic

trapping of atoms in 1985, many different kinds of magnetic atom

traps have been used. At MIT, Dave Pritchard’s group trapped

(Bagnato eft al., 1987) and cooled (Helmerson ef al, 1992) Na

atoms in a linear quadrupole magnetic field with an axial bias field,

similar to the trap first discussed by Ioffe and collaborators (Gott,

Ioffe, and Telkovsky, 1962) in 1962, and later by others (Pritchard,

1983;.Bergeman ef al., 1987). Similar traps were used by the

Kleppner-Greytak group to trap (Hess ef al., 1987) and

evaporatively cool (Masuhura ef a/., 1988) atomic hydrogen, and by

Walraven’s group to trap (van Royen ef a/., 1988) and laser-cool

hydrogen (Setija ef al., 1994). The Ioffe trap has the advantage of

having a non-zero magnetic field at the equilibrium point, in

contrast to the spherical quadrupole, in which the field is zero at the

equilibrium point. The zero field allows the magnetic moment of the

atom to flip (often called Majorana flopping), so that the atom is in

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“a

an untrapped spin state. While this problem did not cause difficulties

in our 1985 demonstration, for colder atoms, which spend more

time near the trap center, it can be a quite severe loss mechanism

(Davis, Mewes, Joffe et al., 1995; Petrich et al., 1995). In 1995,

modifications to the simple quadrupole trap solved the problem of

spins flips near the trap center, and allowed the achievement of

Bose-Einstein condensation (Anderson ef al., 1995; Davis, Mewes,

Andrews ef al., 1995).

DENSITY (cm-3)

i eae ) 0.5 1.0

DETUNING MHz ; TRAP TIME (8)

FIG. 11. (a) Spectra of atoms remaining in the magnetic trap after various times;

(b) decay of number of trapped atoms with time. The open point was taken at

twice the background pressure of the other points.

Optical Molasses

At the same time that we were doing the first magnetic trap

experiments in Gaithersburg, the team at Bell Labs, led by Steve

Chu, was working on a different and extremely important feature of

laser cooling. After a beautiful demonstration in 1978 of the use

of optical forces to focus an atomic beam (Bjorkholm e7 a/., 1978),

the Bell Labs team had made some preliminary attempts to decelerate

an atom beam, and then moved on to other things. Encouraged

by the beam deceleration experiments in Gaithersburg and in

Boulder, Steve Chu reassembled much of that team and set out to

demonstrate the kind of laser cooling suggested in 1975 by Hansch

and Schawlow. [The physical principles behind the Hansch and

Schawlow proposal are, of course, identical to those expressed in the

1975 Wineland and Dehmelt laser cooling proposal. These

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principles had already led to the laser cooling of trapped ions

(Neuhauser e/ al., 1978; Wineland e¢ al., 1978). The foci of Hansch

and Schawlow (1975) and Wineland and Dehmelt (1975), however,

has associated the former with neutral atoms and the latter with ions. |

In fact, the same physical principle of Doppler cooling results in the

compression of the velocity distribution associated with laser

deceleration of an atomic beam [see sections 2 and 3 of Phillips

(1992)]. Nevertheless, in 1985, laser cooling ofa gas of neutral atoms

at rest, as proposed in Hansch and Schawlow (1975), had yet to be

demonstrated.

The idea behind the Hansch and Schawlow proposal is

illustrated in Fig. 12. A gas of atoms, represented here in one

dimension, is irradiated from both sides by laser beams tuned

slightly below the atomic resonance frequency. An atom moving

toward the left sees that the laser beam opposing its motion is

Doppler shifted toward the atomic resonance frequency. It sees that

the laser beam directed along its motion is Doppler shifted further

from its resonance. The atom therefore absorbs more strongly from

the laser beam that opposes its motion, and it slows down. The same

thing happens to an atom moving to the right, so all atoms are slowed

by this arrangement of laser beams. With pairs of laser beams added

along the other coordinate axes, one obtains cooling in three

dimensions. Because of the role of the Doppler Effect in the process,

this 1s now called Doppler cooling.

SLL ae ava’,

DIT ISIE a DUA a

L0SNISNIOIS we OO HWANAIWw

SSNS ILI NS\S VSI

aT BN fio ae a HANNS

ALLL HAAN

SSNS NIL S> SNA

LLY —O<w WAYNIIVYIVY

DLL VI/ A> SNAILS

S\SVNSL VI VACUA Ae

4\S NSIS SI 4AANAY,

FIG. 12. Doppler cooling in one dimension.

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Later treatments (Letokhov ef al., 1977; Neuhauser ef al.,

1978; Stenholm, 1978a; Wineland efa/., 1978; Wineland and Itano,

1979; Javanainen, 1980; Javanainen and Stenholm, 1980b)

recognized that this cooling process leads to a temperature whose

lower limit is on the order of AI, where T is the rate of spontaneous

emission of the excited state (I~! is the excited state lifetime).

The temperature results from an equilibrium between laser

cooling and the heating process arising from the random nature of

both the absorption and emission of photons. The random addition

to the average momentum transfer produces a random walk of the

atomic momentum and an increase in the mean square atomic

momentum. This heating is countered by the cooling force Ff’

opposing atomic motion. The force is proportional to the atomic

velocity, as the Doppler shift is proportional to velocity. In this, the

cooling force is similar to the friction force experienced by a body

moving in a viscous fluid. The rate at which energy is removed by

cooling is F-v, which is proportional to v*, so the cooling rate is

proportional to the kinetic energy. By contrast the heating rate,

proportional to the total photon scattering rate, is independent of

atomic kinetic energy for low velocities. As a result, the heating and

cooling come to equilibrium at a certain value of the average kinetic

energy. This defines the temperature for Doppler cooling, which is

2 het ene

PUY, ) hat = j (+ 2 (1)

where 6 is the angular frequency of the detuning of the lasers from

atomic resonance and vj is the velocity along some axis. This

expression is valid for 3D Doppler cooling in the limit of low

intensity and when the recoil energy f’°k* /2m<«<hilI. Interestingly,

the equilibrium velocity distribution for Doppler cooling is the

Maxwell-Boltzmann distribution. This follows from the fact that the

Fokker-Planck equation describing the damping and heating in laser

cooling is identical in form to the equation that describes collisional

equilibrium of a gas (Stenholm, 1986). Numerical simulations of real

cases, where the recoil energy does not vanish, show that the

distribution is still very close to Maxwellian (Lett ef al., 1989). The

Winter 2016

minimum value of this temperature is called the Doppler cooling limit,

occurring when 6 =-I/2,

All

ae i

B+ Dopp — D) ‘

(2)

The first rigorous derivation of the cooling limit appears to

be by Letokhov, Minogin, and Pavilik (1977) [although the reader

should note that Eq. (32) is incorrectly identified with the rms

velocity]. Wineland and Itano (1979) give derivations for a number

of different situations involving trapped and free atoms and include

the case where the recoil energy is not small but the atoms are in

collisional equilibrium.

The Doppler cooling limit for sodium atoms cooled on the

resonance transition at 589 nm where I’/27z =10 MHz, is 240 uk, and

corresponds to an rms velocity of 30 cm/s along a given axis. The limits

for other atoms and ions are similar, and such low temperatures were

quite appealing. Before 1985, however, these limiting temperatures

had not been obtained in either ions or neutral atoms.

A feature of laser cooling not appreciated in the first

treatments was the fact that the spatial motion of atoms in any

reasonably sized sample would be diffusive. For example, a simple

calculation (Lett ef a/., 1989) shows that a sodium atom cooled to the

Doppler limit has a “mean free path” (the mean distance it moves

before its initial velocity is damped out and the atom is moving with

a different, random velocity) of only 20 um, while the size of the

laser beams doing the cooling might easily be one centimeter. Thus,

the atom undergoes diffusive, Brownian-like motion, and the time

for a laser cooled atom to escape from the region where it is being

cooled is much longer than the ballistic transit time across that

region. This means that an atom is effectively “‘stuck”’ in the laser

beams that cool it. This stickiness, and the similarity of laser cooling

to viscous friction, prompted the Bell Labs group (Chu ef al., 1985)

to name the intersecting laser beams “optical molasses.” At NBS

(Phillips, Prodan, and Metcalf, 1985), we independently used the term

“molasses” to describe the cooling configuration, and the name “‘stuck.”

Note that an optical molasses is not a trap. There is no restoring force

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keeping the atoms in the molasses, only a viscous inhibition of their

escape.

FIG. 13. Release-and-recapture method for temperature measurement.

Using the techniques for chirp cooling an atomic beam

developed at NBS-JILA (Ertmer ef a/l., 1985) and a novel pulsed

beam source, Chu’s team at Bell Labs succeeded in loading cold

sodium atoms into an optical molasses (Chu ef al., 1985). They

observed the expected long “lifetime” (the time required for the atoms

to diffuse out of the laser beams) of the molasses, and they developed

a method, now called “release-and-recapture,’ for measuring the

temperature of the atoms. The method is illustrated in Fig. 13. First,

the atoms are captured and stored in the molasses, where for short

periods of time they are essentially immobile due to the strong

damping of atomic motion [Fig. 13(a)]. Then, the molasses laser beams

are switched off, allowing the atoms to move ballistically away from

the region to which they had originally been viscously confined [Fig.

13(b)]. Finally the laser beams are again turned on, recapturing the

atoms that remain in the intersection (molasses) region [Fig. 13(c)].

From the fraction of atoms remaining after various periods of ballistic

expansion one can determine the velocity distribution and therefore

the temperature of the atoms at the time of release. The measured

temperature at Bell Labs was 240°" kK. [Today one would expect a

much lower temperature; the high temperature observed in this

experiment has since been ascribed to the presence of a stray

magnetic field from an ion pump (Chu, 1997).] The large uncertainty

is due to the sensitive dependence of the analysis on the size and

density distribution of atoms in the molasses, but the result was

satisfyingly consistent with the predicted Doppler cooling limit.

Winter 2016

By the end of 1986, Phil Gould and Paul Lett had joined

our group and we had achieved optical molasses in our laboratory at

NBS, loading the molasses directly from a decelerated beam.

[Today it is also routine to load atoms directly into a magneto-

optical trap (MOT) (Raab ef al., 1987) from an uncooled vapor

(Cable et al., 1990; Monroe ef al., 1990) and then into molasses.] We

repeated the release-and-recapture temperature measurements,

found them to be compatible with the reported measurements of

the Bell Labs group, and we proceeded with other experiments. In

particular, with Paul Julienne, Helen Thorsheim and John Wiener,

we made a 2-focus laser trap and used it to perform the first

measurements of a specific collision process (associative ionization)

with laser cooled atoms (Gould ef a/l., 1988). [Earlier, Steve Chu and

his colleagues had used optical molasses to load a single-focus laser

trap—the first demonstration of an optical trap for atoms (Chu ef al.,

1986).] In a sense, our collision experiment represented a sort of

closure for me because it realized the two-focus trap proposed in

Ashkin’s 1978 paper, the paper that had started me thinking about laser

cooling and trapping. It also was an important starting point for our

group, because it began a new and highly productive line of research

into cold collisions, producing some truly surprising and important

results (Lett ef al., 1991; Lett et al., 1993; Ratliff et al., 1994: Lett er

al, 1995; Walhout-er al, 1995; Jones eral, 11996; Wicsinga ter al,

1996). In another sense, though, that experiment was a detour from

the road that was leading us to a new understanding of optical

molasses and of how laser cooling worked.

lifetime (s)

detuning (linewidths)

FIG. 14. Experimental molasses lifetime (points) and the theoretical decay time

(curve) vs detuning of molasses laser from resonance.

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Sub-Doppler Laser Cooling

During 1987 Gould, Lett and I investigated the behavior of

optical molasses in more detail. Because the temperature was hard

to measure and its measurement uncertainty was large, we

concentrated instead on the molasses lifetime, the time for the atoms

to diffuse out of the intersecting laser beams. We had calculated,

on the basis of the Doppler cooling theory, how the lifetime would

vary as a function of the laser frequency detuning and the laser

intensity. We also calculated how the lifetime should change when

we introduced a deliberate imbalance between the two beams of a

counter-propagating pair. Now we wanted to compare experimental

results with our calculations. The results took us somewhat by

surprise.

Figure 14 shows our measurements (Lett ef al/., 1989) of the

molasses lifetime as a function of laser frequency along with the

predicted behavior according to the Doppler cooling theory. The 1-

D theory did not quantitatively reproduce the observed 3-D

diffusion times, but that was expected. The surprise was the

qualitative differences: the experimental lifetime peaked at a laser

detuning above 3 linewidths, while the theory predicted a peak

below one linewidth. We did not know how to reconcile this

difficulty, and the results for the drift induced by beam imbalance

were also in strong disagreement with the Doppler theory. In our

1987 paper, we described our failed attempts to bring the Doppler

cooling theory into agreement with our data and ended saying

(Gould ef al., 1987): “It remains to consider whether the multiple

levels and sublevels of Na, multiple laser frequencies, or a

consideration of the detailed motion of the atoms in 3-D can explain

the surprising behavior of optical molasses.” This was pure

guesswork, of course, but it turned out to have an element of truth, as

we shall see below.

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MOLASSES

BEAMS

MOLASSES

TTT aa

Boe: al LTPP TTT

PROBE

re LW va BEAM

é \ COLLECTION

ne OPTICS

S DETECTOR

FIG. 15. Time-of-flight method for measuring laser cooling temperatures.

Having seen such a clear discrepancy between the Doppler

cooling theory and the experimental results, with no resolution in

sight, we, aS experimentalists, decided to take more data. Paul Lett

argued that we should measure the temperature again, this time as

a function of the detuning, to see if it, too, would exhibit behavior

different from that predicted by the theory. We felt, however, that

the release-and-recapture method, given the large uncertainty

associated with it in the past, would be unsuitable. Hal Metcalf

suggested a different approach, illustrated in Fig. 15.

In this time-of-flight (TOF) method, the atoms are first

captured by the optical molasses, then released by switching off the

molasses laser beams. The atom cloud expands ballistically,

according to the distribution of atomic velocities. When atoms

encounter the probe laser beam, they fluoresce, and the time

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distribution of fluorescence gives the time-of-flight distribution for

atoms arriving at the probe. From this the temperature can be

deduced. Now, with a team that included Paul Lett, Rich Watts,

Chris Westbrook, Phil Gould, as well as Hal Metcalf and myself,

we implemented the TOF temperature measurement. In our

experiment, the probe was placed as close as | cm from the center

of the molasses, which had a radius of about 4.5 mm. At the lowest

expected temperature, the Doppler cooling limit of 240 uK for Na

atoms, a significant fraction of the atoms would have been able to

reach the probe, even with the probe above the molasses. For

reasons of convenience, we did put the probe beam above the

molasses, but we saw no fluorescence from atoms reaching the probe

after the molasses was turned off. We spent a considerable time

testing the detection system to be sure that everything was working

properly. We deliberately “squirted” the atoms to the probe beam

by heating them with a pair of laser beams in the horizontal plane,

and verified that such heated atoms reached the probe and produced

the expected time-of-flight signal,

1.0

0.8;

0.6

0.4

Fluorescence signal

0.2

0.0

Time (ms)

FIG. 16. The experimental TOF distribution (points) and the predicted distribution

curves for 40 WK and 240 LK (the predicted lower limit of Doppler cooling). The

band around the 40 uK curve reflects the uncertainty in the measurement of the

geometry of the molasses and probe.

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Finally, we put the probe under the molasses. When we did,

we immediately saw the TOF signals, but were reluctant to accept

the conclusion that the atoms were colder than the Doppler cooling

theory predicted, until we had completed a detailed modeling of the

TOF signals. Figure 16 shows a typical TOF distribution for one of

the colder observed temperatures, along with the model

predictions. The conclusion was inescapable: Our atoms had a

temperature of about 40 uK, much colder than the Doppler cooling

limit of 240 UK. They had had insufficient kinetic energy to reach

the probe when it was placed above the molasses. As clear as this

was, we were apprehensive. The theory of the Doppler limit was

simple and compelling. In the limit of low intensity, one could derive

the Doppler limit with a few lines of calculations (see for example,

Lett et al., 1989); the most complete theory for cooling a two-level

atom (Gordon and Ashkin, 1980) did not predict a cooling limit any

lower. Of course, everyone recognized that sodium was not a two-

level atom, but it had seemed unlikely that it made any significant

difference (our speculation in Gould ef a/., 1987, notwithstanding).

At low laser intensity the temperature depends on the laser detuning

and the linewidth of the transition. Since the linewidth is identical

for all possible transitions in the Na D2 manifold, and since the

cooling transition [3S1/2 (7 =2)—3P3/2 (F=3)] was well separated

from nearby transitions, and all the Zeeman levels were degenerate,

it seemed reasonable that the multilevel structure was unimportant in

determining the cooling limit.

As it turned out, this was completely wrong. At the time,

however, the Doppler limit seemed to be on firm theoretical ground,

and we were hesitant to claim that it was violated experimentally.

Therefore, we sought to confirm our experimental results with other

temperature measurement methods. One of these was to refine the

“release-and-recapture” method described above. The large

uncertainties in the earlier measurements (Chu ef al., 1985) arose

mainly from uncertainties in the size of the molasses and the recapture

volume. We addressed that problem by sharply aperturing the molasses

laser beams so the molasses and recapture volumes were well defined.

We also found that it was essential to include the effect of gravity in

the analysis (as we had done already for the TOF method). Because

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released atoms fall, the failure to recapture atoms could be interpreted

as a higher temperature if gravity is not taken into account.

Another method was the “fountain” technique. Here we

exploited our initial failure to observe a TOF signal with the probe

above the molasses. By adjusting the height of the probe, we

could measure how high the atoms could go before falling back

under the influence of gravity. Essentially, this allowed us to

measure the atoms’ kinetic energy in terms of their gravitational

potential energy, a principle very different from the TOF method.

Finally, we used the “shower” method. This determined how far

the atoms spread in the horizontal direction as they fell following

release from the molasses. For this, we measured the fluorescence

from atoms reaching the horizontal probe laser beam at different

positions along that beam. From this transverse position distribution,

we could get the transverse velocity distribution and therefore the

temperature.

(The detailed modeling of the signals expected from the

various temperature measurement methods was an essential

element in establishing that the atomic temperature was well below

the Doppler limit. Rich Watts, who had come to us from Hal

Metcalf’s lab and had done his doctoral dissertation with Carl

Wieman, played a leading role in this modeling. Earlier, with

Wieman, he had introduced the use of diode lasers in laser cooling.

With Metcalf, he was the first to laser cool rubidium, the element

with which Bose-Einstein condensation was first achieved. He

was a pioneer of laser cooling and continued a distinguished

scientific career at NIST after completing his postdoctoral studies in

our group. Rich died in 1996 at the age of 39, and is greatly missed.)

While none of the additional methods proved to be as accurate

as the TOF technique (which became a standard tool for studying

laser cooling temperatures), each of them showed the temperature

to be significantly below the Doppler limit. Sub-Doppler

temperatures were not the only surprising results we obtained. We

also (as Paul Lett had originally suggested) measured the

temperature as a function of the detuning from resonance of the

molasses laser. Figure 17 shows the results, along with the

Winter 2016

prediction of the Doppler cooling theory. The dependence of the

temperature on detuning is strikingly different from the Doppler

theory prediction, and recalls the discrepancy evident in Fig. 14. Our

preliminary study indicated that the temperature did not depend on

the laser intensity [although later measurements (Lett ef al., 1989;

Phillips ef al, 1989; Salomon et al., 1990) showed that the

temperature actually had a linear dependence on intensity]. We

observed that the temperature depended on the polarization of the

molasses laser beams, and was highly sensitive to the ambient

magnetic field. Changing the field by 0.2 mT increased the

temperature from 40 UK to 120 UK when the laser was detuned 20

MHz from resonance [later experiments (Lett e/ a/l., 1989) showed

even greater effects]. This field dependence was _ particularly

surprising, considering that transitions were being Zeeman shifted

on the order of 14 MHz/mT, so the Zeeman shifts were much less

than either the detuning or the 10 MHz transition linewidth. Armed

with these remarkable results, in the early spring of 1988 we sent

a draft of the paper (Lett ez a/., 1988) describing our measurements

to a number of experimental and theoretical groups working on laser

cooling. I also traveled to a few of the leading laser cooling labs to

describe the experiments in person and discuss them. Many of our

colleagues were skeptical, as well they might have been,

considering how surprising the results were. In the laboratories of

Claude Cohen-Tannoudji and of Steve Chu, however, the response

was: “Let’s go into the lab and find out if it is true.” Indeed, they

soon confirmed sub-Doppler temperatures with their own

measurements and they began to work on an understanding of how

such low temperatures could come about. What emerged from

these studies was a new concept of how laser cooling works, an

understanding that is quite different from the original Hansch-

Schawlow and Wineland-Dehmelt picture.

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400

= 300

® 100

0 10 20 30 40

Detuning (MHz)

FIG. 17. Dependence of molasses temperature on laser detuning (points)

compared to the prediction of Doppler cooling theory (curve). The different

symbols represent different molasses-to-probe separations.

During the spring and summer of 1988 our group was in close

contact with Jean Dalibard and Claude Cohen-Tannoudji as they

worked out the new theory of laser cooling and we continued our

experiments. Their thinking centered on the multilevel character of

the sodium atom, since the derivation of the Doppler mit was

rigorous for a two-level atom. The sensitivity of temperature to

magnetic field and to laser polarization suggested that the Zeeman

sublevels were important, and this proved to be the case. Steve Chu

(now at Stanford) and his colleagues followed a similar course, but

the physical image that Dalibard and Cohen-Tannoudji developed

has dominated the thinking about multilevel laser cooling. It

involves a combination of multilevel atoms, polarization gradients,

light shifts and optical pumping. How these work together to

produce laser cooling is illustrated in simple form in Fig. 18, but

the reader should see the Nobel Lectures of Cohen-Tannoudji and

Chu along with the more detailed papers (Dalibard and Cohen-

Tannoudji, 1989; Ungar ef a/., 1989; Cohen-Tannoudji and Phillips,

1990; Cohen-Tannoud}j1, 1992).

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m= -1/2 +1/2

O- O+ O-

FIG. 18. (a) Interfering, counter-propagating beams having orthogonal, linear

polarizations create a polarization gradient. (b) The different Zeeman sublevels

are shifted differently in light fields with different polarizations; optical pumping

tends to put atomic population on the lowest energy level, but non-adiabatic motion

results in “Sisyphus” cooling.

Figure 18(a) shows a 1-D set of counter-propagating beams

with equal intensity and orthogonal, linear polarizations. The

interference of these beams produces a standing wave whose

polarization varies on a sub wavelength distance scale. At points in

space where the linear polarizations of the two beams are in phase

with each other, the resultant polarization is linear, with an axis

that bisects the polarization axes of the two individual beams.

Where the phases are in quadrature, the resultant polarization is

circular and at other places the polarization is elliptical. An atom

in such a standing wave experiences a fortunate combination of light

shifts and optical pumping processes.

Because of the differing Clebsch-Gordan coefficients

governing the strength of coupling between the various ground and

excited sublevels of the atom, the light shifts of the different

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sublevels are different, and they change with polarization (and

therefore with position). Figure 18(b) shows the sinusoidal variation

of the ground-state energy levels (reflecting the varying light shifts or

dipole forces) of a hypothetical Jg=1/2—>Jce=3/2 atomic system.

Now imagine an atom to be at rest at a place where the polarization

is circular oO as at z=A/8 in Fig. 18(a). As the atom absorbs light with

negative angular momentum and radiates back to the ground states,

it will eventually be optically pumped into the mg=-1/2 ground

state, and simply cycle between this state and the excited me=-3/2

state. For low enough intensity and large enough detuning we can

ignore the time the atom spends in the excited state and consider

only the motion of the atom on the ground state potential. In the

mg=-1/2 state, the atom is in the lower energy level at z =//8, as

shown in Fig. 18(b). As the atom moves, it climbs the potential hill

of the mg=-1/2 state, but as it nears the top of the hill at z=3//8,

the polarization of the light becomes 6° and the optical pumping

process tends to excite the atom in such a way that it decays to the

mg= + 1/2 state. In the mg= + 1/2 state, the atom 1s now again at the

bottom of a hill, and it again must climb, losing kinetic energy, as

it moves. The continual climbing of hills recalls the Greek myth of

Sisyphus, so this process, by which the atom rapidly slows down

while passing through the polarization gradient, is called Sisyphus

cooling. Dalibard and Cohen-Tannoudji (1985) had already

described another kind of Sisyphus cooling, for two-level atoms, so

the mechanism and the name were already familiar. In both kinds of

Sisyphus cooling, the radiated photons, in comparison with the

absorbed photons, have an excess energy equal to the light shift. By

contrast, in Doppler cooling, the energy excess comes irom the

Doppler shift.

The details of this theory were still being worked out in the

summer of 1988, the time of the International Conference on

Atomic Physics, held that year in Paris. The sessions included talks

about the experiments on sub-Doppler cooling and the new ideas to

explain them. Beyond that, I had lively discussions with Dalibard

and Cohen-Tannoudji about the new theory. One insight that

emerged from those discussions was an understanding of why we had

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observed such high sensitivity of temperature to magnetic field: It

was not the size of the Zeeman shift compared to the linewidth or

the detuning that was important. Rather, when the Zeeman shift was

comparable to the much smaller (~1 MHz) light shifts and optical

pumping rates, the cooling mechanism, which depended on these

phenomena, would be disturbed. We now suggested a crucial test:

the effect of the magnetic field should be reduced if the light

intensity were higher. From Paris, I telephoned back to the lab in

Gaithersburg and urged my colleagues to perform the appropriate

measurements.

500

400

go 300

® 200

100

-200 -100 0 100 200

Magnetic Field (uT)

FIG. 19. Temperature vs magnetic field in a 3-D optical molasses. Observation

of lower temperature at higher intensity when the magnetic field was high

provided an early confirmation of the new theory of sub-Doppler cooling

~The results were as we had hoped. Figure 19 shows

temperature as a function of magnetic field for two different light

intensities. At magnetic fields greater than 100 uT (1 gauss), the

temperature was lower for higher light intensity, a reversal of the usual

linear dependence of temperature and intensity (Lett ef al, 1989;

Salomon ef al., 1990). We considered this to be an important early

confirmation of the qualitative correctness of the new theory,

confirming the central role played by the light shift and the magnetic

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sublevels in the cooling mechanism. Joined by Steve Rolston and

Carol Tanner we (Paul Lett, Rich Watts, Chris Westbrook, and myself)

carried out additional studies of the behavior of optical molasses,

providing qualitative comparisons with the predictions of the new

theory. Our 1989 paper (Lett et al.), “Optical Molasses” summarized

these results and contrasted the predictions of Doppler cooling with

the new theory. Steve Chu’s group also published additional

measurements at the same time (Weiss ef al., 1989). Other, even more

detailed measurements in Paris (Salomon eft a/l., 1990) (where I was

very privileged to spend the academic year of 1989-1990) left little

doubt about the correctness of the new picture of laser cooling. In those

experiments we cooled Cs atoms to 2.5 uK. It was a truly exciting

time, when the developments in the theory and the experiments were

pushing each other to better understanding and lower temperatures.

Around this time, Jan Hall [whose pioneering work in chirp cooling

(Ertmer ef al., 1985) had done so much to launch the explosive activity

a few years before] commented that being in the field of laser cooling

was an experience akin to being in Paris at the time of the

Impressionists. Figure 20 symbolizes the truth of that comment.

Optical Lattices

In 1989 we began a different kind of measurement on laser

cooled atoms, a measurement that was to lead us to a new and highly

fruitful field of research. We had always been a bit concerned that

all of our temperature measurements gave us information about

the velocity distribution of atoms after their release from the optical

molasses and we wanted a way to measure the temperature in situ.

Phil Gould suggested that we measure the spectrum of the light

emitted from the atoms while they were being cooled. For

continuous, single frequency irradiation at low intensity and large

detuning, most of the fluorescence light scattered from the atoms

should be “elastically” scattered, rather than belonging to the

“Mollow triplet” of high-intensity resonance fluorescence (Mollow,

1969). This elastically scattered light will be Doppler shifted by the

moving atoms and its spectrum should show a Doppler broadening

characteristic of the temperature of the atomic sample. The spectrum

will also contain the frequency fluctuations of the laser itself, but

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these are relatively slow for a dye laser, so Gould suggested a

heterodyne method of detection, where the fluorescent light is

mixed on a photodiode with local oscillator light derived from the

molasses laser, producing a beat signal that is free of the laser

frequency fluctuations.

FIG. 20. (Color) Hal Metcalf, Claude Cohen-Tannoudji and the author on the

famous bridge in Monet’s garden at Giverny, ca. 1990.

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The experiment was not easy, and it worked mainly because

of the skill and perseverance of Chris Westbrook. An example of

the surprising spectrum we obtained (Westbrook ef al., 1990) is

shown in Fig. 21. The broad pedestal corresponded well to what we

expected from the time-of-flight temperature measurement on a

similar optical molasses, but the narrow central peak was a puzzle.

After rejecting such wild possibilities as the achievement of Bose-

Einstein condensation (Fig. 21 looks remarkably similar to velocity

distributions in partially Bose-condensed atomic gases) we realized

that the answer was quite simple: we were seeing line-narrowing from

the Lamb-Dicke effect (Dicke, 1953) of atoms localized to less than

a wavelength of light.

Atoms were being trapped by the dipole force in periodically

spaced potential wells like those of Fig. 18(b). We knew from both

theory and experiments that the thermal energy of the atoms was less

than the light shifts producing the potential wells, so it was quite

reasonable that the atoms should be trapped. Confined within a

region much less than a wavelength of light, the emitted spectrum

shows a suppression of the Doppler width, the Lamb-Dicke effect,

which is equivalent to the Méssbauer effect. This measurement

(Westbrook et al., 1990) marked the start of our interest in what are

now called optical lattices: spatially periodic patterns of light-shift-

induced potential wells in which atoms are trapped and well

localized. It also represents a realization of the 1968 proposal of

Letokhov to reduce the Doppler width by trapping atoms in a

standing wave.

Joined by Poul Jessen, who was doing his Ph.D. research in

our lab, we refined the heterodyne technique and measured the

spectrum of Rb atoms in a 1-D laser field like that of Fig. 18(a).

Figure 22 shows the results (Jessen ef a/l., 1992), which display well-

resolved sidebands around a central, elastic peak. The sidebands are

separated from the elastic peak by the frequency of vibration of

atoms in the 1-D potential wells. The sideband spectrum can be

interpreted as spontaneous Raman scattering, both Stokes and anti-

Stokes, involving transitions that begin on a given quantized

vibrational level for an atom bound in the optical potential and end

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on a higher vibrational level (the lower sideband), the same level

(elastic peak) or a lower level (the higher sideband). We did not

see sidebands in the earlier experiment in a 3-D, six-beam optical

molasses (Westbrook ef a/., 1990) at least in part because of the lack

of phase stability among the laser beams (Grynberg ef al., 1993). We

have seen well-resolved sidebands in a 3-D, four-beam lattice

(Gatzke et al., 1997).

Density

(Arbitrary Units)

Spectral

- 1 -0.5 0 0.5 1

Relative Frequency (MHz)

FIG. 21. Heterodyne spectrum of fluorescence from Na atoms in optical molasses.

The broad component corresponds to a temperature of 84 UK, which compares well

with the temperature of 87 UK measured by TOF. The narrow component indicates

a sub-wavelength localization of the atoms.

Fluorescence (arb. units)

-200 -100 0 100 200

frequency (kHz)

FIG. 22. Vertical expansion of the spectrum emitted by Rb atoms in a 1-D

optical lattice. The crosses are the data of Jessen et al. (1992); the curve is a first-

principles calculation of the spectrum (Marte ef al., 1993). The calculation has no

adjustable parameters other than an instrumental broadening. Inset: unexpanded

spectrum.

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The spectrum of Fig. 22 gives much information about the

trapping of atoms in the potential wells. The ratio of sideband

intensity to elastic peak intensity gives the degree of localization, the

ratio of the two sideband intensities gives the temperature, and the

spacing of the sidebands gives the potential well depth. Similar,

but in many respects complementary, information can be obtained

from the absorption spectrum of such an optical lattice, as illustrated

by the experiments performed earlier in Paris (Verkerk ef al., 1992).

The spectrum of Fig. 22 can be calculated from first principles

(Marte ef al., 1993) and the comparison of the experimental and

theoretical spectra shown provides one of the most detailed

confirmations of our ability to predict theoretically the behavior of

laser cooled atoms.

In our laboratory, we have continued our studies of optical

lattices, using adiabatic expansion to achieve temperatures as low

as 700 nK (Kastberg ef al., 1995), applying Bragg scattering to study

the dynamics of atomic motion (Birkl ef al., 1995; Phillips, 1997;

Raithel, Birkl, Kastberg eft al., 1997; Raithel, Birkl, Phillips, and

Rolston, 1997), and extending heterodyne spectral measurements to

3-D (Gatzke et al., 1997). The Paris group has also continued to

perform a wide range of experiments on optical lattices (Louis ef

al., 1993; Meacher ef al., 1994; Verkerk et al., 1994; Meacher ef al.,

1995), as have a number of other groups all over the world.

The optical lattice work has emphasized that a typical atom is

quite well localized within its potential well, implying a physical

picture rather different from the Sisyphus cooling of Fig. 18, where

atoms move from one well to the next. Although numerical

calculations give results in excellent agreement with experiment in

the case of lattice-trapped atoms, a physical picture with the

simplicity and power of the original Sisyphus picture has not yet

emerged. Nevertheless, the simplicity of the experimental behavior

makes one think that such a picture should exist and remains to be

found. The work of Castin (1992) and Castin e7# a/. (1994) may point

the way to such an understanding.

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Conclusion

I have told only a part of the story of laser cooling and trapping

at NIST in Gaithersburg, and I have left out most of the work that

has been done in other laboratories throughout the world. I have told

this story from my personal vantage point as an experimentalist in

Gaithersburg, as I saw it unfold. The reader will get a much more

complete picture by also reading the Nobel lectures of Steve Chu

and Claude Cohen-Tannoudji. For the work in my lab, I have tried

to follow the thread that leads from laser deceleration and cooling

of atomic beams (Phillips and Metcalf, 1982; Prodan ef al., 1982;

Phillips and Prodan, 1984; Prodan eft al., 1985) to magnetic trapping

(Migdall et al., 1985), the discovery of sub-Doppler cooling (Lett

et al., 1988; Lett et al., 1989), and the beginnings of optical lattice

studies (Westbrook ef al., 1990; Jessen et al., 1992). Topics such as

later studies of lattices, led by Steve Rolston, and collisions of cold

atoms, led by Paul Lett, have only been mentioned, and other areas

such as the optical tweezer work (Mammen e/a/., 1996; Helmerson

etal., 1997) led by Kris Helmerson have been left out completely.

The story of laser cooling and trapping is still rapidly

unfolding, and one of the most active areas of progress is in

applications. These include “practical” applications like atomic

clocks, atom interferometers, atom lithography, and optical tweezers,

as well as “scientific” applications such as collision studies, atomic

parity non-conservation, and Bose-Einstein condensation (BEC).

(The latter 1s a particularly beautiful and exciting outgrowth of laser

cooling and trapping. Since the 1997 Nobel festivities, our laboratory

has joined the growing number of groups having achieved BEC,

as shown in Fig. 23.) Most of these applications were completely

unanticipated when laser cooling started, and many would have been

impossible without the unexpected occurrence of sub-Doppler

cooling.

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FIG. 23. (Color) One of the most recent applications of laser cooling and

magnetic trapping is Bose-Einstein condensation in an atomic vapor. The figure

shows a series of representations of the 2-D velocity distribution of a gas of Na

atoms at different stages of evaporative cooling through the BEC transition. The

velocity distribution changes from a broad thermal one (left) to include a narrow,

condensate peak (middle), and finally to be nearly pure condensate (right). The

data were obtained in our laboratory in February of 1998, by L. Deng, E.

Hagley, K. Helmerson, M. Kozuma, R. Lutwak, Y. Ovchinnikov, S. Rolston,

J. Wen and the author. Our procedure was similar to that used in the first such

observation of BEC, in Rb, at NIST/JILA in 1995 (Anderson ef al., 1995).

Laser cooling and trapping has from its beginnings been

motivated by a blend of practical applications and basic curiosity.

When I started doing laser cooling, I had firmly in mind that |

wanted to make better atomic clocks. On the other hand, the

discovery of sub-Doppler cooling came out of a desire to

understand better the basic nature of the cooling process.

Nevertheless, without sub-Doppler cooling, the present generation

of atomic fountain clocks would not have been possible.

I hesitate to predict where the field of laser cooling and

trapping will be even a few years from now. Such predictions have

often been wrong in the past, and usually too pessimistic. But |

firmly believe that progress, both in practical applications and in

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basic understanding, will be best achieved through research driven by

both aims.

Acknowledgments

I owe a great debt to all of the researchers in the many

laboratories around the world who have contributed so much to the

field of laser cooling and trapping of neutral atoms. Their friendly

competition and generous sharing of understanding and insights has

inspired me and educated me in an invaluable way. Very special

thanks go to those researchers with whom I have been privileged

to work here in Gaithersburg: to Hal Metcalf, who was part of the

laser cooling experiments from the start, through most of the work

described in this paper; to postdocs John Prodan, Alan Migdall,

Phil Gould, Chris Westbrook, and Rich Watts, whose work led our

group to the discovery of sub-Doppler cooing, and who moved on

to distinguished careers elsewhere; to Paul Lett, Steve Rolston, and

Kris Helmerson who also were pivotal figures in the development

of laser cooling and trapping in Gaithersburg, who have formed the

nucleus of the present Laser Cooling and Trapping Group (and who

have graciously provided considerable help in the preparation of

this manuscript); and to all the other postdocs, visitors and students

who have so enriched our studies here. To all of these, I am thankful,

not only for scientific riches but for shared friendship.

I know that I share with Claude Cohen-Tannoudji and with

Steve Chu the firm belief that the 1997 Nobel Prize in Physics honors

not only the three of us, but all those other researchers in this field

who have made laser cooling and trapping such a rewarding and

exciting subject. I want to thank NIST for providing and sustaining

the intellectual environment and the resources that have nurtured

a new field of research and allowed it to grow from a few

rudimentary ideas into a major branch of modern physics. I also

thank the U.S. Office of Naval Research, which provided crucial

support when I and my ideas were unproven, and which continues

to provide invaluable support and encouragement.

There are many others, friends, family and teachers who

have been of great importance. I thank especially my wife and

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daughters who have supported and encouraged me and provided that

emotional and_= spiritual grounding that makes achievement

worthwhile. Finally I thank God for providing such a wonderful and

intriguing world for us to explore, for allowing me to have the

pleasure of learning some new things about it, and for allowing me

to do so in the company of such good friends and colleagues.

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Andreev, S., V. Balykin, V. Letokhov, and V. Minogin, 1981, “Radiative slowing

and reduction of the energy spread of a beam of sodium atoms to 1.5 K in an

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Lett. 34, 442 (1981)].

Ashkin, A., 1970, “Atomic-beam deflection by resonance-radiation pressure,” Phys.

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Ashkin, A., 1978, “Trapping of atoms by resonance radiation pressure,” Phys. Rev.

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Askar’ yan, G. A., 1962, “Effects of the gradient of a strong electromagnetic beam

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Bagnato, V., G. Lafyatis, A. Martin, E. Raab, R. Ahmad-Bitar, and D. E. Pritchard,

1987, “Continuous slowing and trapping of neutral atoms,” Phys. Rev. Lett.

58, 2194.

Balykin, V., 1980, “Cyclic interaction of Na atoms with circularly polarized laser

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for neutral atoms,” Phys. Rev. A 35, 1535.

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“Observation of quantum jumps in a single atom,” Phys. Rev. Lett. 57, 1699.

Birkl, G., M. Gatzke, I. H. Deutsch, S. L. Rolston, and W. D. Phillips, 1995,

“Bragg scattering from atoms in optical lattices,” Phys. Rev. Lett. 75, 2823.

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pressure,” Phys. Rev. Lett. 41, 1361.

Winter 2016

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Systems in Quantum Optics, edited by J. Dalibard, J.-M. Raimond, and J.

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Cohen-Tannoudji, C., and W. D. Phillips, 1990, Phys. Today 43 (10), 33.

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motion in laser light: the dipole force revisited,” J. Opt. Soc. Am. B 2, 1707.

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Washington Academy of Sciences

Gatzke, M., G. Birkl, P. S. Jessen, A. Kastberg, S. L. Rolston, and W. D. Phillips,

1997, “Temperature and localization of atoms in 3D optical lattices,” Phys. Rev.

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1961, Salzburg, Austria (International Atomic Energy Agency, Vienna), Nucl.

Fusion Suppl. 1962, pt. 3, p. 1045.

Gould, P: L., P. D. Vett; P.S.. Julienne; W. D. Phillips, H. R. Thorshem, and. J.

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sodium atoms,” Phys. Rev. Lett. 60, 788.

Gould, P. L., P. D. Lett, and W. D. Phillips, 1987, “New measurements with optical

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Clin. Chem. 43, 379.

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Winter 2016

Javanainen, J., and S. Stenholm, 1980b, “Broad band resonant light pressure II:

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Jessen, P. J., C. Gerz, P. D. Lett, W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and

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Jones, K., P. Julienne, P. Lett, W. Phillips, E. Tiesinga, and C. Williams, 1996,

“Measurement of the atomic Na(3P) lifetime and of retardation in the interaction

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Kastberg, A., W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and P. S. Jessen, 1995,

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Phys. Rev. Lett, 71,2200.

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Phys. Rev. Lett. 61, 169.

Washington Academy of Sciences

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Europhys. Lett. 21, 13.

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evaluate potent polyvalent inhibitors of virus-cell adhesion,” Chemistry &

Biology 3, 757.

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Winter 2016

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Washington Academy of Sciences

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101, 2638.

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Winter 2016

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46.

Washington Academy of Sciences

Bose-Einstein Condensation in a Dilute Gas, the

First 70 Years and Some Recent Experiments’

E. A. Cornell and C. E. Wieman

JILA, University of Colorado and National Institute of Standards and Technology,

and Department of Physics, University of Colorado, Boulder, Colorado

Abstract

Bose-Einstein condensation, or BEC, has a long and rich history

dating from the early 1920s. In this article we will trace briefly

over this history and some of the developments in physics that

made possible our successful pursuit of BEC in a gas. We will

then discuss what was involved in this quest. In this discussion we

will go beyond the usual technical description to try and address

certain questions that we now hear frequently, but are not

covered in our past research papers. These are questions along

the lines of: How did you get the idea and decide to pursue it?

Did you know it was going to work? How long did it take you

and why? We will review some our favorites from among the

experiments we have carried out with BEC. There will then be a

brief encore on why we are optimistic that BEC can be created

with nearly any species of magnetically trappable atom.

Throughout this article we will try to explain what makes BEC in

a dilute gas so interesting, unique, and experimentally

challenging.”

THE NOTION OF BOSE STATISTICS dates back to a 1924 paper in

which Satyendranath Bose used a statistical argument to derive the

blackbody photon spectrum (Bose, 1924). Unable to publish his

work, he sent it to Albert Einstein, who translated it into German

! The 2001 Nobel Prize in Physics was shared by E. A. Comell, Wolfgang Ketterle, and

C. E. Wieman. Reprinted from Reviews of Modern Physics, 74, 2002.

This article is our ‘‘Nobel Lecture’’ and as such takes a relatively personal approach to

the story of the development of experimental Bose-Einstein condensation. For a

somewhat more scholarly treatment of the history, the interested reader is referred to E.

A. Cornell, J. R. Ensher, and C. E. Wieman, “Experiments in dilute atomic Bose-

Einstein condensation in Bose-Einstein Condensation in Atomic Gases,”? Proceedings of

the International School of Physics “Enrico Fermi’’ Course CXL, edited by M. Inguscio,

S. Stringari, and C. E. Wieman (Italian Physical Society, 1999), pp. 15-66, which is also

available as cond-mat/9903109. For a reasonably complete technical review of the three

years of explosive progress that immediately followed the first observation of BEC,

we recommend reading the above article in combination with the corresponding review

from Ketterle, cond-mat/9904034.

Winter 2016

and got it published. Einstein then extended the idea of Bose’s

counting statistics to the case of non-interacting atoms (Einstein,

1924, 1925). The result was Bose-Einstein statistics. Einstein

immediately noticed a peculiar feature of the distribution of the

atoms over the quantized energy levels predicted by these statistics.

At very low but finite temperature a large fraction of the atoms would

go into the lowest energy quantum state. In his words, “A separation

is effected; one part condenses, the rest remains a saturated ideal

gas”? (Einstein, 1925). This phenomenon we now know as Bose-

Einstein condensation. The condition for this to happen is that the

phase-space density must be greater than approximately unity, in

natural units. Another way to express this is that the de Broglie

wavelength, Aas, of each atom must be large enough to overlap with

its neighbor, or more precisely, n/;, > 2.61.

This prediction was not taken terribly seriously, even by

Einstein himself, until Fritz London (1938) and Laszlo Tisza (1938)

resurrected the idea in the mid-1930s as a possible mechanism

underlying superfluidity in liquid helium 4. Their work was the first

to bring out the idea of BEC displaying quantum behavior on a

macroscopic size scale, the primary reason for much of its current

attraction. Although it was a source of debate for decades, it is now

recognized that the remarkable properties of superconductivity and

superfluidity in both helium 3 and helium 4 are related to BEC,

even though these systems are very different from the ideal gas

considered by Einstein.

The appeal of the exotic behavior of superconductivity and of

superfluidity, along with that of laser light, the third common system

in which macroscopic quantum behavior is evident, provided much

of our motivation in 1990 when we decided to pursue BEC in a gas.

These three systems all have fascinating counterintuitive behavior

arising from macroscopic occupation of a single quantum state. Any

physicist would consider these phenomena among the most

remarkable topics in physics. In 1990 we were confident that the

addition of a new member to the family would constitute a major

3 English translation of Einstein’s quotes and the historical interpretation are from Pais

(1982), Subtle is the Lord...

Washington Academy of Sciences

contribution to physics. (Only after we succeeded did we realize that

the discovery of each of the original Macroscopic Three had been

recognized with a Nobel Prize, and we are grateful that this trend

has continued!) Although BEC shares the same _ underlying

mechanism with these other systems, it seemed to us that the

properties of BEC in a gas would be quite distinct. It is far more

dilute and weakly interacting than liquid helium superfluids, for

example, but far more strongly interacting than the non-interacting

light in a laser beam. Perhaps BEC’s most distinctive feature (and

this was not something we sufficiently appreciated, in 1990) is the

ease with which its quantum wave function may be directly

observed and manipulated. While neither of us was to read C. E.

Hecht’s prescient 1959 paper (Hecht, 1959) until well after we had

observed BEC, we surely would have taken his concluding

paragraph as our marching orders:

The suppositions of this note rest on the possibility of securing,

say by atomic beam techniques, substantial quantities of electron-

spin-oriented H, T and D atoms. Although the experimental

difficulties would be great and the relaxation behavior of such

spin-oriented atoms essentially unknown, the possibility of

opening arich new field for the study of superfluid properties in

both liquid and gaseous states would seem to demand _ the

expenditure of maximum experimental effort.*

In any case, by 1990 we were awash in motivation. But this

motivation would not have carried us far, had we not been able to

take advantage of some key recent advances in science and

technology, in particular, the progress in laser cooling and trapping

and the extensive achievements of the spin-polarized-hydrogen

community.

However, before launching into that story, it 1s perhaps

worthwhile to reflect on just how exotic a system of indistinguishable

particles truly is, and why BEC in a gas is such a daunting

experimental challenge. It is easy at first to accept that two atoms can

be so similar one to the other as to allow no possibility of telling them

4 Emphasis ours.

Winter 2016

apart. However, confronting the physical implications of the concept

of indistinguishable bosons can be troubling. For example, if there

are ten bosonic particles to be arranged in two microstates of a

system, the statistical eight of the configuration with ten particles in

one state and zero in the other is exactly the same as the weight of

the configuration with five particles in one state, five in the other.

This 1:1 ratio of statistical weights is very counterintuitive and rather

disquieting. The corresponding ratio for distinguishable objects, such

as socks in drawers that we observe every day, is 1:252, profoundly

different from 1:1. In the second of Einstein’s two papers (Einstein,

1925; Pais, 1982) on Bose- Einstein statistics, Einstein comments

that ““The... molecules are not treated as statistically independent...”’,

and the differences between distinguishable and indistinguishable

state counting “. .. express indirectly a certain hypothesis on a

mutual influence of the molecules which for the time being is of a

quite mysterious nature.” This mutual influence is no less mysterious

today, even though we can readily observe the variety of exotic

behavior it causes such as the well-known enhanced probability for

scattering into occupied states and, of course, Bose-Einstein

condensation.

Vapor a

{

Forbidden

wa (Liquid

*~~"Helium)

Log Temperature

Log Density

FIG. 1. Generic phase diagram common to all atoms: dotted line, the boundary

between non-BEC and BEC; solid line, the boundary between allowed and

forbidden regions of the temperature-density space. Note that at low and

intermediate densities, BEC exists only in the thermodynamically forbidden

regime.

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au)

Not only does the Bose-Einstein phase transition offend our

sensibilities as to how particles ought best to distribute themselves,

it also runs counter to an unspoken assumption that a phase

transition somehow involves thermodynamic stability. In fact, the

regions immediately above and immediately below the transition in

dilute-gas experiments are both deep in the thermodynamically

forbidden regime. This point is best made by considering a

qualitative phase diagram (Fig. 1), which shows the general features

common to any atomic system. At low density and high temperature,

there is a vapor phase. At high density there are various condensed

phases. But the intermediate densities are thermodynamically

forbidden, except at very high temperatures. The Bose-condensed

region of the n-7 plane is utterly forbidden, except at such high

densities that (with one exception) all known atoms or molecules

would form a crystalline lattice, which would rule out Bose

condensation. The single exception, heltum, remains a liquid below

the BEC transition. However, reaching BEC under dilute conditions

(say, at densities 10 or 100 times lower than conventional liquid

helium) is as thermodynamically forbidden to helium as it is to any

other atom.

Of course, forbidden is not the same as impossible; indeed,

to paraphrase an old Joseph Heller joke, if it were really

impossible, they wouldn’t have bothered to forbid it. It comes

down in the end to differing time scales for different sorts of

equilibrium. A gas of atoms can come into kinetic equilibrium via

two-body collisions, whereas it requires three-body collisions to

achieve chemical equilibrium (i.e., to form molecules and thence

solids). At sufficiently low densities, the two- body rate will

dominate the three-body rate, and a gas will reach kinetic

equilibrium, perhaps in a metastable Bose-Einstein condensate,

long before the gas finds its way to the ultimately stable solid-state

condition. The need to maintain metastability usually dictates a

more stringent upper limit on density than does the desire to create

a dilute system. Densities around 107° cm”, for instance, would be

a hundred times more dilute than a condensed-matter helium

superfluid. But creating such a gas is quite impractical even at an

additional factor of 1000 lower density, say 10'’ cm?, when

Winter 2016

metastability times would be on the order of a few microseconds

more realistic are densities on the order of 10'* cm®. The low

densities mandated by the need to maintain long-lived

metastability in turn make necessary the achievement of still lower

temperatures if one 1s to reach BEC.

Thus the great experimental hurdle that must be overcome to

create BEC in a dilute gas is to form and keep a sample that is so

deeply forbidden. Since our subsequent discussion will focus only

on BEC in dilute gases, we shall refer to this simply as BEC in the

sections below and avoid endlessly repeating “in a dilute gas.”

Efforts to make a dilute BEC in an atomic gas were sparked

by Stwalley and Nosanow (1976). They argued that spin-polarized

hydrogen had no bound states and hence would remain a gas down to

zero temperature, and so it would be a good candidate for BEC. This

stimulated a number of experimental groups (Silvera and Walraven,

1980; Hardy et al., 1982; Hess et al., 1983; Johnson et al., 1984) in the

late 1970s and early 1980s to begin pursuing this idea using traditional

cryogenics to cool a sample of polarized hydrogen. Spin-polarized

hydrogen was first stabilized by Silvera and Walraven in 1980, and

by the mid-1980s spin-polarized hydrogen had been brought within a

factor of 50 of condensing (Hess ef al., 1983). These experiments were

performed in a dilution refrigerator, in a cell in which the walls were

coated with superfluid liquid helium as a nonstick coating for the

hydrogen. The hydrogen gas was compressed using a piston-in-cylinder

arrangement (Bell et al., 1986) or inside a helium bubble (Sprik ef al.,

1985). These attempts failed, however, because when the cell was

made very cold the hydrogen stuck to the helium surface and

recombined. When one tried to avoid that problem by warming the

cell sufficiently to prevent sticking, the density required to reach BEC

was correspondingly increased, which led to another problem. The

requisite densities could not be reached because the rate of three- body

recombination of atoms into hydrogen molecules goes up rapidly

with density and the resulting loss of atoms limited the density (Hess,

1986).

Stymied by these problems, Harold Hess (Hess, 1986) from the

MIT hydrogen group realized that magnetic trapping of atoms (Migdall

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et al., 1985; Bagnato et al., 1987) would be an improvement over a cell.

Atoms in a magnetic trap have no contact with a physical surface and

thus the surface-recombination problem could be circumvented.

Moreover, thermally isolated atoms in a magnetic trap would allow

cooling by evaporation to far lower temperatures than previously

obtained. In a remarkable paper, Hess (1986) laid out most of the

important concepts of evaporative cooling of trapped atoms for the

attainment of BEC. Let the highest-energy atoms escape from the

trap, and the mean energy, and thus the temperature, of the remaining

atoms will decrease. For a dilute gas in an inhomogeneous potential,

decreasing the temperature will decrease the occupied volume. One

can thus actually increase the density of the remaining atoms by

removing atoms from the sample. The all-important (for BEC)

phase-space density is dramatically increased as this happens

because density is rising while temperature 1s decreasing. The Cornell

University hydrogen group also considered evaporative cooling

(Lovelace et al., 1985). By 1988 the MIT group had demonstrated

these virtues of evaporative cooling of magnetically trapped spin-

polarized hydrogen. By 1991 they obtained, at a temperature of 100

°K, a density that was only a factor of 5 below BEC (Doyle, 1991a).

Further progress was limited by dipolar relaxation, but perhaps more

fundamentally by loss of signal-to-noise, and the difficulty of

measuring the characteristics of the coldest and smallest clouds

(Doyle, 1991b). Evaporative work was also performed by the

Amsterdam group (Luiten ef a/., 1993).

At roughly the same time, but independent from the hydrogen

work, an entirely different type of cold-atom physics and technology

was being developed. Laser cooling and trapping has been reviewed

elsewhere (Arimondo ef al/., 1991; Chu, 1998; Cohen-Tannoudji,

1998; Phillips, 1998), but here we mention some of the highlights

most relevant to our work. The idea that laser light could be used to

cool atoms was suggested in early papers by Wineland and Dehmelt

(1975), by Hansch and Schawlow (1975), and by Letokhov’s group

(Letokhov, 1968). Early optical force experiments were performed

by Ashkin (Bjorkholm e7 a/., 1978). Trapped ions were laser-cooled

at the University of Washington (Neuhauser e/ a/., 1978) and at the

National Bureau of Standards (now NIST) in Boulder (Wineland ef

Winter 2016

al., 1978). Atomic beams were deflected and slowed in the early

1980s (Andreev ef al., 1981; Ertmer et al., 1985; Prodan ef al., 1985).

Optical molasses, where the atoms are cooled to very low

temperatures by six perpendicular intersecting laser beams, was first

studied at Bell Labs (Chu et al., 1985). Measured temperatures in

the early molasses experiments were consistent with the so-called

Doppler limit, which amounts to a few hundred microkelvin in

most alkalis. Light was first used to hold (trap) atoms using the

dipole force exerted by a strongly focused laser beam (Chu ef a/.,

1986). In 1987 and 1988 there were two major advances that became

central features of the method of creating BEC. First, a practical

spontaneous-force trap, the magneto-optical trap (MOT) was

demonstrated (Raab et al., 1987); and second, it was observed that

under certain conditions, the temperatures in optical molasses are in

fact much colder than the Doppler limit (Lett e¢ al., 1988; Chu e7 al.,

1989; Dalibard et al., 1989). The MOT had the essential elements

needed for a widely useful optical trap: 1t required relatively modest

amounts of laser power, 1t was much deeper than dipole traps, and

it could capture and hold relatively large numbers of atoms. These

were heady times in the laser-cooling business. With experiment

yielding temperatures mysteriously far below what theory would

predict, it was clear that we all lived under the authority of a

munificent God.

During the mid-1980s one of us (Carl) began investigating how

useful the technology of laser trapping and cooling could become for

general use in atomic physics. Originally this took the form of just

making it cheaper and simpler by replacing the expensive dye lasers

with vastly cheaper semiconductor lasers, and then searching for

ways to allow atom trapping with these low-cost but also low-power

lasers (Pritchard ef a/l., 1986; Watts and Wieman, 1986). With the

demonstration of the MOT and sub-Doppler molasses Carl’s group

began eagerly studying what physics was limiting the coldness

and denseness of these trapped atoms, with the hope of extending

the limits further. They discovered that several atomic processes

were responsible for these limits. Light-assisted collisions were

found to be the major loss process from the MOT as the density

increased (Sesko ef a/., 1989). However, even before that became a

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serious problem, the light pressure from reradiated photons limited

the density (Walker ef al., 1990; Sesko etal, 1991). At about the

same time, the sub-Doppler temperatures of molasses found by

Phillips, Chu, and Cohen-Tannoudji were shown to be due to a

combination of light-shifts and optical pumping that became

known as Sysiphus cooling (Dalibard and Cohen-Tannoudji, 1989).

Random momentum fluctuations from the scattered photons limit the

ultimate temperature to about a factor of 10 above the recoil limit.

In larger samples, the minimum temperature was higher yet, because

of the multiple scattering of the photons. While carrying out studies

on the density limits of MOT’s Carl’s group also continued the

effort in technology development. This resulted in the creation of

a useful MOT in a simple glass vapor cell (Monroe ef a/., 1990),

thereby eliminating the substantial vacuum chamber required for the

slowed atomic beam loading that had previously been used.

Seeking to take advantage of the large gains in phase-space

density provided by the MOT while avoiding the limitations

imposed by the undesirable effects of photons, Carl and his student

Chris Monroe decided to try loading the cold MOT atoms into a

magnetic trap (Monroe ef al, 1990; see Fig. 2). This worked

remarkably well. Because further cooling could be carried out as the

atoms were transferred between optical and magnetic trap it was

possible to get very cold samples, the coldest that had been produced

at that time. More importantly, these were not optical molasses

samples that were quickly disappearing but rather magnetically

trapped samples that could be held and studied for extended periods.

These samples were about a hundred times colder than any previous

trapped atom samples, with a correspondingly increased phase-

space density. This was a satisfying achievement, but as much as the

result itself, it was the relative simplicity of the apparatus required

that inspired us (including now Eric Cornell, who joined the project

as a postdoc in 1990) to see just how far we could push this marriage

of laser cooling and trapping and magnetic trapping.

Previous laser traps involved expensive massive laser systems

and large vacuum chambers for atomic beam precooling. Previous

magnetic traps for atoms were usually (Bagnato ef a/., 1987; Doyle,

Winter 2016

1991) extremely complex and bulky (often with superconducting

coils) because of the need to have sufficiently large depths and

strong confinement. Laser traps and magnetic traps were both

somewhat heroic experiments individually, to be undertaken only by

a select handful of well-equipped AMO laboratories. The prospect of

trying to get both traps working, and working well, in the same room

and on the same day, was daunting. However, in the first JILA

magnetic trap experiment our laser sources were simple diode lasers,

the vacuum system was a small glass vapor cell, and the magnetic

trap was just a few turns of wire wrapped around it. This magnetic

field was adequate because of the low temperatures of the laser-

cooled and trapped samples. Being able to produce such cold and

trapped samples in this manner encouraged one to fantasize wildly

about possible things to do with such an atom sample. Inspired by

the spin-polarized hydrogen work, our fantasizing quickly turned to

the idea of evaporative cooling further to reach BEC. It would require

us to increase the phase-space density by 5 orders of magnitude, but

since we had just gained about 15 orders of magnitude almost for

free with the vapor cell MOT, this did not seem so daunting.

The JILA vapor-cell MOT (Fig. 3), with its superimposed ion

pump trap, introduced a number of ideas that are now in common use

in the hybrid trapping business (Monroe et a/., 1990; Monroe, 1992):

(1) Vapor-cell (rather than beam) loading, (11) fused-glass rather than

welded-steel architecture, (111) extensive use of diode lasers, (iv)

magnetic coils located outside the chamber, (v) overall chamber

volume measured in cubic centimeters rather than liters, (vi)

temperatures measured by imaging an expanded cloud, (vii)

magnetic-field curvatures calibrated in situ by observing the

frequency of dipole and quadrupole (sloshing and pulsing) cloud

motion, (vill) the basic approach of a MOT and a magnetic trap

which are spatially superimposed (indeed, which often share some

magnetic coils) but temporally sequential, and (1x) optional use of

additional molasses and optical pumping sequences inserted in time

between the MOT and magnetic trapping stages. It is instructive to

note how a modern, loffe-Pritchard-based BEC device (Fig. 4)

resembles its ancestor (Fig. 3).

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As we began to think about applying the technique of

evaporative cooling with hydrogen to our very cold alkali atoms we

looked carefully at the hydrogen work and its lessons. When viewed

from our 1990 perspective the previous decade of work on polarized

hydrogen provided a number of important insights. It was clear that

the unique absence of any bound states for spin- polarized hydrogen

was actually not an important issue (other than its being the catalyst

for starting the entire field, of course!). Bound states or not, a very

cold sample of spin-polarized hydrogen, like every other gas, has a

lower-energy state to which it can go, and its survival depends on the

preservation of metastability. For hydrogen the lower-energy state is

a solid, although from an experimental point of view the rate-limiting

process is the formation of diatomic molecules (with appropriately

reoriented spins). Given that all atomic gases are only metastable at

the BEC transition point, the real experimental issue becomes: How

well can one preserve the requisite metastability while still cooling

sufficiently far to reach BEC?

=——uiT, 1

‘AY ‘hae

= bh

\ :

}

FIG. 2. Chris Monroe examines an early hybrid MOT- magnetic trap

apparatus [Color].

Winter 2016

The realization that metastability was the key experimental

challenge one should focus on was probably at least as important

to the attainment of BEC as any of the experimental techniques we

subsequently developed to actually achieve it. The work on

hydrogen provided an essential guide for evaluating and tackling this

challenge. It provided us with a potential cooling technique

(evaporative cooling of magnetically trapped atoms) and mapped out

many of the processes by which a magnetically trapped atom can be

lost from its metastable state.

FIG. 3. The glass vapor cell and magnetic coils used in early JILA efforts to

hybridize laser cooling and magnetic trapping (see Monroe ef a/., 1990). The glass

tubing is 2.5 cm in diameter. The Ioffe current bars have been omitted for clarity.

FIG. 4. Modern MOT and magnetic trap apparatus, used by Cornish ef ai.,

2000 [Color].

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The hydrogen work made it clear that it was all an issue of

good versus bad collisions. The good collisions are elastic collisions

that re-thermalize the atoms during evaporation. The more

collisions there are, the more quickly and efficiently one can cool.

The bad collisions are the inelastic collisions that quench the

metastability. Hydrogen had already shown that three-body

recombination collisions and dipole spin-flip collisions were the

major inelastic culprits. The fact that hydrogen researchers were fairly

close to reaching BEC was also a strong encouragement. It meant

that the goal was not ridiculously distant and that one only had to

do a little better in the proportion of good to bad collisions to

succeed.

The more we thought about this, the more we began to

suspect that our heavy alkali atoms would likely have more favorable

collision properties than hydrogen atoms and thus have a good

chance of success. Although knowledge of the relevant collision

cross sections was totally nonexistent at that time, we were able to

come up with arguments for how the cross sections might scale

relative to hydrogen. These are discussed in more detail below in the

section discussing why collisional concerns make it likely that BEC

can be created in a large number of different species. Here we will

just give a brief summary consistent with our views circa 1990. The

dipole spin-flip collisions that limited hydrogen involve spin-spin

interactions and thus could be expected to be similar for the alkalis

and for hydrogen because the magnetic moments are all about the

same. The good collisions needed for evaporative cooling, however,

should be much larger for heavy alkalis with their fat fluffy electron

clouds than for hydrogen. The other villain of the hydrogen effort,

three-body recombination, was a total mystery, but because it goes as

density cubed while the good elastic collisions go as density squared,

it seemed as if we should always be able to find a sufficiently low-

density and low-temperature regime to avoid it (see Monroe, 1992).

As a minor historical note, we might point out that during

these considerations we happily ignored the fact that the

temperatures required to achieve BEC in a heavy alkali gas are far

colder than those needed for the same density of hydrogen. The

Winter 2016

critical temperature for ideal-gas BEC is inversely proportional to

the mass. It was clear that we would need to cool to well under a

microkelvin, and a large three-body recombination rate would have

required us to go to possibly far lower temperatures. To someone

coming from a traditional cryogenics background this would (and

probably did) seem like sheer folly. The hydrogen work had been

pushing hard for some years at the state of the art in cryogenic

technology, and here we proposed to happily jump far beyond that.

Fortunately we were coming to this from an AMO background in a

time when temperatures achieved by laser cooling were dropping

through the floor. Optimism was in the air. In fact, we later

discovered optimism can take one only so far: There were actually

considerable experimental difficulties, and further cooling came at

some considerable effort and a five-year delay. Nevertheless, it is

remarkable that with evaporative cooling a magnetically trapped

sample of atoms, surrounded on all sides by a 300-K glass cell, can be

cooled to reach temperatures of only a few nanokelvin, and

moreover it looks quite feasible to reach even colder temperatures.

General collisional considerations gave us some hope that the

evaporative cooling hybrid trap approach with alkali atoms would

get us to BEC, or, if not, at least reveal some interesting new

physics that would prevent it. Nonetheless, there were powerful

arguments against pursuing this. First, our 1990-era arguments in

favor of it were based on some very fuzzy intuition; there were no

collision data or theories to back it up and there were strong voices

in disagreement. Second, the hydrogen experiments seemed to be on

the verge of reaching BEC, and in fact we thought it was likely that

if BEC could be achieved they would succeed first. However, our

belief in the virtues of our technology really carried the day in

convincing us to proceed. With convenient lasers in the near-IR, and

with the good optical access of a room- temperature glass cell,

detection sensitivity could approach single-atom capability. We

could take pictures of only a few thousand trapped atoms and

immediately know the energy and density distribution. If we wanted

to modify our magnetic trap it only required a few hours winding and

installing a new coil of wires. This was a dramatic contrast with the

hydrogen experiments that, lke all state-of-the-art cryogenics

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experiments, required an apparatus that was the better part of two

stories, and the time to modify it was measured in (large) fractions

of a year. Also, atomic hydrogen was much more difficult to detect

and so the diagnostics were far more limited. This convinced us that

although hydrogen would likely succeed first, our hybrid trap

approach with easily observed and manipulated alkali samples would

be able to carry out important science and so was well worth

pursuing in its own right.

From the very beginning in 1990, our work on BEC was

heavily involved with cold atomic collisions. This was somewhat

ironic since previously both of us had actively avoided the large fraction

of AMO work on the subject of atomic collisions. Atomic collisions

at very cold temperatures 1s now a major branch of the discipline

of AMO physics, but at the end of the 1980s there were almost no

experimental data, and what there was came in fact from the spin-

polarized hydrogen experiments (Gillaspy ef al., 1989). There was

theoretical work on hydrogen from Shlyapnikov and Kagan (Kagan ef

al., 1981, 1984), and from Silvera and Verhaar (Lagendiyk ef al.,

1986). An early paper by Pritchard (1986) includes estimates on low-

temperature collisional properties for alkalis. His estimates were

extrapolations from room- temperature results, but in retrospect,

several were surprisingly accurate. As we began to work on

evaporative cooling, much of our effort was devoted to determining

the sizes of all the relevant good and bad collision cross sections. Our

efforts were helped by the theoretical efforts of Boudewijn Verhaar,

who was among the first to take our efforts seriously and attempt to

calculate the rates in question. Chris Greene also provided us with

some useful theoretical estimates.

Starting in 1990 we carried out a series of experiments

exploring various magnetic traps and measuring the relevant collision

cross sections. As this work proceeded we developed a far better

understanding of the conditions necessary for evaporative cooling and

a much clearer understanding of the relevant collisional issues (Monroe

et al., 1993; Newbury et al., 1995). Our experimental concerns evolved

accordingly. In the early experiments (Monroe ef al., 1990, 1993;

Cornell et al., 1991; Monroe, 1992) a number of issues came up that

Winter 2016

continue to confront all BEC experiments: the importance of aligning

the centers of the MOT and the magnetic trap, the density-reducing

effects of mode-mismatch, the need to account carefully for the

(previously ignored) force of gravity, heating (and not merely loss)

from background gas collisions, the usefulness of being able to turn off

the magnetic fields rapidly, the need to synchronize many changes

in laser status and magnetic fields together with image acquisition, an

appreciation for the many issues that can interfere with accurate

determinations of density and temperature by optical methods, either

florescence or absorption imaging, and careful stabilization of

magnetic fields. The mastery of these issues in these early days made

it possible for us to proceed relatively quickly to quantitative

measurements with the BEC once we had it.

In 1992 we came to realize that dipolar relaxation in alkalis

should in principle not be a limiting factor. As explained in the final

section of this article, collisional scaling with temperature and

magnetic field is such that, except 1n pathological situations, the

problem of good and bad collisions in the evaporative cooling of

alkalis is reduced to the ratio of the elastic collision rate to the rate

of loss due to imperfect vacuum; dipolar relaxation and three-body

recombination can be finessed, particularly since our preliminary

data showed they were not enormous. It was reassuring to move

ahead on efforts to evaporate with the knowledge that, while we

were essentially proceeding in the dark, there were not as many

monsters in the dark as we had originally imagined.

It rapidly became clear that the primary concerns would be

having sufficient elastic collision rate in the magnetic trap and

sufficiently low background pressure to have few background

collisions that removed atoms from the trap. To accomplish this it

was clear that we needed higher densities in the magnetic trap than we

were getting from the MOT. Our first effort to increase the density

two years earlier was based on a multiple- loading scheme (Cornell

et al., 1991). Multiple MOT- loads of atoms were launched in moving

molasses, optically pumped into an untrapped Zeeman level, focused

into a magnetic trap, then optically re-pumped into a trapped level. The

re-pumping represented the necessary dissipation, so that multiple

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loads of atoms could be inserted in a continuously operating magnetic

trap. In practice, each step of the process involved some losses, and

the final result was disappointing. Later, however, as discussed below,

we resurrected the idea of multiple loading from one MOT to another

to good advantage (Gibble ef al., 1995; Myatt et al., 1996). This is

now a technique currently in widespread practice.

In addition to building up the initial density we realized that

the collision rate could be dramatically increased by, after loading into

a magnetic trap, compressing the atoms by further increasing the

curvature of the confining magnetic fields. In a harmonic trap, the

collision rate after adiabatic compression scales as the final confining

frequency squared (Monroe, 1992). This method is discussed by

Monroe (1992) and was implemented first in early ground-state

collisional work (Monroe ef al., 1993).

In fall of 1992, Eric’s postdoctoral appointment concluded,

and, after a tour through the job market, he decided to take the

equivalent of an assistant professor position at JILA/NIST. He

decided to use his startup money to build a new experimental

apparatus that would be designed to put these ideas together to make

sure evaporation worked as we expected. Meanwhile, we continued

to pursue the possibility of enhanced collision cross sections in

cesium using a Feshbach resonance. At that point our Monte Carlo

simulations said that a ratio of about 150 elastic collisions per trap

lifetime was required to achieve runaway evaporation. This is the

condition where the elastic collision rate would continue to increase

as the temperature decreased, and hence evaporation would

continue to improve as the temperature was reduced. We also had

reasonable determinations of the elastic collision cross sections.

So the plan was to build a simple quadrupole trap that would

allow very strong squeezing to greatly enhance the collision rate,

combined with a good vacuum system in order to make sure

evaporative cooling worked as expected. Clearly, there was much to

be gained by building a more tightly confining magnetic trap, but

the requirement of adequate optical access for the MOT, along with

engineering constraints on power dissipation, made the design

problem complicated.

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When constructing a trap for weak-field-seeking atoms, with the

aim of confining the atoms to a spatial size much smaller than the size

of the magnets, one would like to use linear gradients. In that case,

however, one is confronted with the problem of the minimum in

the magnitude of the magnetic fields (and thus of the confining

potential) occurring at a local zero in the magnetic field. This zero

represents a hole in the trap, a site at which atoms can undergo

Majorana transitions (Majorana, 1931) and thus escape from the

trap. If one uses the second-order gradients from the magnets to

provide the confinement, there is a marked loss of confinement

strength. This scaling is discussed by Petrich e¢ al. (1995). We knew

that once the atoms became cold enough they would leak out the

hole in the bottom of the trap, but the plan was to go ahead and get

evaporation and worry about the hole later. We also recognized that

even with successful evaporative cooling, and presuming we could

solve the issue of the hole in the quadrupole trap, there was still the

question of the sign of scattering length, which must be positive to

ensure the stability of a large condensate.

In setting up the new apparatus Eric chose to use rubidium.

Given the modulo arithmetic that goes into determining a scattering

length, it seemed fair to treat the scattering lengths of different

isotopes as statistically independent events, and rubidium with its

two stable isotopes offered two rolls of the dice for the same laser

system. Eric then purchased a set of diode lasers for the rubidium

wavelength, but of course we kept the original cesium-tuned diode

lasers. The wavelengths of cesium and of the two rubidium isotopes

are sufficiently similar that in most cases one can use the same optics.

Thus we preserved the option of converting from one species to

another in a matter of weeks. The chances then of Nature’s

conspiring to make the scattering length negative, for both hyperfine

levels, for all three atoms, seemed very small.

Progress in cold collisions, particularly the experiment and

theory of photo-associative collisions, had moved forward so

rapidly that by the time we had evaporatively cooled rubidium to

close to BEC temperatures a couple of years later there existed, at

the 20% level, values for several of the elastic scattering lengths. In

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particular, we knew that it was positive for the 2,2 state of Rb-87

(Thorsheim ef al., 1987; Lett et al, 1993; Miller e¢ al., 1993;

Abraham efal., 1995; Gardner et al., 1995; McAlexander efal., 1995).

Our original idea for the quadrupole trap experiment was to

pulse a burst of rubidium into our cell, where we would catch a large

sample in the MOT and then hold it as the residual rubidium was

quickly pumped away, leaving a long trap lifetime. We, particularly

Eric’s postdoc, Mike Anderson, spent many frustrating months

discovering how difficult this seemingly simple idea was to actually

implement in practice. The manner in which rubidium interacted

with glass and stainless-steel surfaces conspired to make this so

difficult we finally gave up. We ended up going with a far-from-

optimum situation of working with extremely low rubidium pressure

and doing our best at maximizing the number of atoms captured in

the MOT from this feeble vapor and enhancing the collision rate for

those relatively few atoms as much as possible. We recognized that

this was a major compromise, but we had been trying to evaporate

for some time, and we were getting impatient! We had no stomach

for building another apparatus just to see evaporation. Fortunately

we were able to find two key elements to enhance the MOT loading

and density. First was the use of a dark-spot MOT in which there is

a hole in the center of the MOT beams so the atoms are not excited.

This technique had been demonstrated by Ketterle (Ketterle ef al.,

1993) as a way to greatly enhance the density of atoms in a MOT

under conditions of a very high loading rate. The number of atoms

we could load in our vapor cell MOT with very low rubidium vapor

was determined by the loading rate over the loss rate. In this case the

loss rate was the photo-associative collisions we had long before

found to be important for losses from MOT’s. The dark-spot

geometry reduced this two-body photo-associative loss in part

because in our conditions 1t reduced the density of atoms in the

MOT (Anderson ef al., 1994).

Using this approach we were able to obtain 10° atoms in the

MOT collected out of a very low vapor background (so that

magnetic trap lifetime was greater than 100 s). The second key

element was the invention of the compressed MOT (CMOT), a

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technique for substantially enhancing the density of atoms in the

MOT on a transient basis. For the CMOT, the MOT was filled and

then the field gradient and laser detuning were suddenly changed to

greatly suppress the multiple photon scattering. This produced much

higher densities and clouds whose shape was a much better match

to the desired shape of the cloud in the magnetic trap. This was a

very transient effect because the losses from the MOT were much

larger under these conditions, but that was not important; the

atoms needed only to be held for the milliseconds required before

they were transferred to the magnetic trap (Petrich ef al., 1994; see

Fig. 5). With these improvements and a quadrupole trap that

provided substantial squeezing, we were able to finally demonstrate

evaporative cooling in rubidium.

Cooling by evaporation is a process found throughout Nature.

Whether the material being cooled is an atomic nucleus or the

Atlantic Ocean, the rate of natural evaporation and the minimum

temperature achievable are limited by the particular fixed value of the

work function of the evaporating substance. In magnetically

confined atoms, no such limit exists, because the work function is

simply the height of the lowest point in the rim of the confining

potential. Hess (1986) pointed out that, by perturbing the confining

magnetic fields, one could make the work function of a trap

arbitrarily low; as long as favorable collisional conditions persist

there is no lower limit to the temperatures attainable in this forced

evaporation.

Pritchard (Pritchard ef a/., 1989) pointed out that evaporation

could be performed more conveniently if the rim of the trap were

defined by an rf-resonance condition, rather than simply by the

topography of the magnetic field; experimentally, his group made

first use of position-dependent rf transitions to selectively transfer

magnetically trapped sodium atoms between Zeeman levels and

thus characterized their temperature (Martin ef a/l., 1988). In our

experiment we used Pritchard’s technique of an rf field to selectively

evaporate.

It was a great relief to see evaporative cooling of laser

precooled, magnetically trapped atoms finally work, as we had been

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anticipating it would for so many years. Unfortunately, it worked

exactly as well, but no better, than we had anticipated. The atoms

were cooled to about 40 UK and then disappeared, at just the

temperature we had estimated they would be lost, through the hole

in the bottom of the quadrupole trap. Eric came up with an idea that

solved this problem. It was a design for a new type of trap that

required relatively little modification to the apparatus and so was

quickly implemented. This was the Time Orbiting Potential (TOP)

trap in which a small rotating magnetic field was added to the

quadrupole field (Petrich et al., 1995). This moved the field zero in

an orbit faster than the atoms could follow. It was the perfect solution

to our problem.

Mike Anderson, another postdoc, Wolfgang Petrich, and

graduate student Jason Ensher quickly implemented this design.

Their efforts were spurred on by the realization that there were

several other groups who had now demonstrated or were known to

be on the verge of demonstrating evaporative cooling in alkalis in

the pursuit of BEC. The TOP design worked well, and the samples

were cooled far colder, in fact too cold for us to reliably measure. We

had been measuring temperature simply by looking at the spatial

size of the cloud in the magnetic trap. As the temperature was

reduced the size decreased, but we were now reaching temperatures

so low that the size had reached the resolution limit of the optical

system. We saw dramatic changes in the shapes of the images as the

clouds became very small, but we knew that a variety of diffraction

and aberration effects could greatly distort images when the sample

size became only a few wavelengths in size, so our reaction to these

shapes was muted, and we knew we had to have better diagnostics

before we could have meaningful results. Here we were helped by

our long experience in studying various trapped clouds over the

years. We already knew the value of turning the magnetic trap off to

let the cloud expand and then imaging the expanded cloud to get

a measure of the momentum distribution in the trap. Since the trap

was harmonic, the momentum distribution and the original density

distribution were nearly interchangeable. Unfortunately, once the

magnetic field was off, the atoms not only expanded but also simply

fell under the influence of gravity. We found that the atoms tended to

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fall out of the field of view of our microscope before they had

sufficiently expanded. The final addition to the apparatus was a

supplementary magnetic coil, which provided sufficient field gradient

to cancel the effects of gravity while minimizing any perturbation to

the relative ballistic trajectories of the expanding atoms.

m4 he

FIG. 5. Wolfgang Petrich working on CMOT [Color].

Anderson, Ensher, and a new graduate student, Mike

Matthews (Fig. 6), worked through a weekend to install the

antigravity coil and, after an additional day or two of trial and error,

got the new field configuration shimmed up. By June 5, 1995 the

new technology was working well and we began to look at the now

greatly expanded clouds. To our delight, the long-awaited two-

component distribution was almost immediately apparent (Fig. 7)

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ie)

when the samples were cooled to the regime where BEC was

expected. The excitement was tempered by the concern that after so

many years of anticipating two component clouds as a signature of

BEC, we might be fooling ourselves.

FIG. 6. From left, Mike Anderson, Debbie Jin, Mike Matthews, and Jason

Ensher savor results of early BEC experiments [Color].

Almost from the beginning of the search for BEC, it was

recognized (Lovelace and Tommila, 1987) that as the sample started

to condense, there would be a spike in the density and momentum

distributions corresponding to the macroscopic population of the

ground state. This would show up as a second component on top of

the much broader normal thermal distribution of uncondensed atoms.

This was the signature we had been hoping to see from our first days

of contemplating BEC. The size of the BEC component in these first

observations also seemed almost too good to be true. In those days it

was known that in the much higher density of the condensate, three-

body recombination would be a more dominant effect than in the

lower-density uncondensed gas. For hydrogen it was calculated that

the condensed component could never be more than a few percent

of the sample. The three-body rate constants were totally unknown

for alkali atoms at that time, but because of the H results it still

seemed reasonable to expect the condensate component might only

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be a modest fraction of the total sample. But in our first samples we

saw it could be nearly 100%! In the light of the prevailing myth

of unattainability that had grown up around BEC over the years, our

observations seemed too good to be true. We were experienced

enough to know that when results in experimental physics seem too

good to be true, they almost always are! We worried that in our

enthusiasm we might confuse the long-desired BEC with some

spurious artifact of our imaging system.

However, our worries about the possibility of deluding

ourselves were quickly and almost entirely alleviated by the

anisotropy of the BEC cloud. This was a very distinctive signature

of BEC, the credibility of which was greatly enhanced to us by the

fact that it first revealed itself in the experiment, and then we

recognized its significance, rather than vice versa. It was a somewhat

fortuitous accident that the TOP trap provided a distinctly

anisotropic trapping potential, since we did not appreciate its

benefits until we saw the BEC data. A normal thermal gas (in the

collisionally thin limit) released from an anisotropic potential will

spread out isotropically. This is required by the equipartition

theorem. However, a Bose-Einstein condensate 1s a quantum wave

and so its expansion 1s governed by a wave equation. The more

tightly confined direction will expand the most rapidly, a

manifestation of the uncertainty principle. Seeing the BEC

component of our two-component distribution display just this

anisotropy, while the broader uncondensed portion of the sample

observed at the same time, with the same imaging system, remained

perfectly isotropic (as shown in Fig. 8), provided the crucial piece

of corroborating evidence that this was the long-awaited BEC. By

coincidence we were scheduled to present progress reports on our

efforts to achieve BEC at three international conferences in the few

weeks following these observations (Anderson ef al., 1996). Nearly

all the experts in the field were represented at one or more of these

conferences, and the data were sufficient to convince the most

skeptical of them that we had truly observed BEC. This consensus

probably facilitated the rapid refereeing and publication of our

results.

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- {00 nk

JTL A-June 1998

FIG. 7. Three density distributions of the expanded clouds of rubidium atoms at

three different temperatures. The appearance of the condensate is apparent as

the narrow feature in the middle image. On the far right, nearly all the atoms in

the sample are in the condensate. The original experimental data were two-

dimensional black and white shadow images, but these images have been

converted to three dimensions and given false color density contours [Color].

FIG. 8. Looking down on the three images of Figure 7 (Anderson ef al., 1995).

The condensate in B and C is clearly elliptical in shape [Color].

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In the original TOP-trap apparatus we were able to obtain

so-called pure condensates of a few thousand atoms. By pure

condensates we meant that nearly all the atoms were in the

condensed fraction of the sample.

Samples of this size were easily large enough to image. Over

the few months immediately following the original observation, we

undertook the process of a technological shoring up of the machine,

until the machine reached the level of reliability necessary to crank

out condensate after reproducible condensate. This set the stage for

the first generation of experiments characterizing the properties of

the condensate, most notably the condensate excitation studies

discussed below.

Although by 1995 and 1996 we were able to carry out a

number of significant BEC experiments with the original TOP-trap

machine, even by 1994, well before the original condensates were

observed, we had come to realize the limitations of the single-cell

design. Our efforts to modulate the vapor pressure were not very

successful, which forced us to operate at a steady-state rubidium

vapor pressure. Choosing the value of vapor pressure at which to

operate represented a compromise between our need to fill the

vapor-cell MOT with as many atoms as possible and our need to have

the lifetime in the magnetic trap as long as possible. The single-cell

design also compelled us to make a second compromise, this time

over the size of the glass cell. The laser beams of the MOT enter

the cell through the smooth, flat region of the cell; the larger the

glass cell, the larger the MOT beams, and the more atoms we could

herd into the MOT from the room-temperature background vapor.

On the other hand, the smaller the glass cell, the smaller the radii

of the magnetic coils wound round the outside of the cell, and the

stronger the confinement provided by the magnetic trap. Hans

Rohner in the JILA specialty shop had learned how (Rohner, 1994)

to create glass cells with the minimum possible wasted area. But

even with the dead space between the inner diameter of the

magnetic coils and the outer diameter of the clear glass windows

made as small as it could be, we were confronted with an

unwelcome tradeoff.

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Thus, in 1994, in parallel with our efforts to push as hard as

we could toward BEC in our original, single-cell TOP trap, we began

working on a new technology that would avoid this painful tradeoff.

This approach was a modified version of our old multiple loading

scheme in which many loads from a MOT were transferred to a

magnetic trap in a differentially pumped vacuum chamber. That

approach had been defeated by the difficulty in transferring atoms

from MOT to magnetic trap without losing phase-space density.

There was no dissipation in the magnetic trap to compensate for a

slightly too hard or too soft push from one trap to the other. This made

us recognize the importance of having dissipation in the second

trap, and so we went to a system in which atoms were captured in a

large-cell MOT in a region of high rubidium pressure, and then

transferred through a small tube into a second, small-cell MOT in

a low-pressure region. This eliminated the previous disadvantages

while preserving the advantages of multiple loading to get much

larger numbers of trapped atoms in a low-vacuum region. The

approach worked well, particularly when we found that simple strips

of plastic refrigerator magnet material around the outside of the

transfer tube between the two traps provided an excellent guide to

confine the atoms as they were pushed from one trap to the other

(Myatt et al., 1996).

With this scheme we were still able to use inexpensive low-

power diode lasers to obtain about one hundred times more atoms in

the magnetic trap than in our single MOT-loaded TOP magnetic trap

and with a far longer lifetime; we saw trap lifetimes up to 1000 s in

the double MOT magnetic trap. This system started working in 1996

and it marked a profound difference in the ease with which we could

make BEC (Myatt et al., 1997). In the original BEC experiment

everything had to be very well optimized to achieve the conditions

necessary for runaway evaporative cooling and thereby BEC. In the

double MOT system there were orders of magnitude to spare. Not

only did this allow us to routinely obtain million-atom pure

condensates, but it also meant that we could dispense with the dark-

spot optical configuration with its troublesome alignment. We could

be much less precise with many other aspects of the experiment as well.

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The first magnetic trap we used with the double-MOT BEC

machine was not a TOP trap, but instead was our old baseball-style

loffe-Pritchard trap. The baseball coil trap is rather complementary

to the TOP trap in that each has unique capabilities. For example,

the geometry of the TOP trap potential can be changed over a wide

range, although the range of de fields is quite limited. In contrast, the

geometry of the baseball coil trap potential can be varied only by

small amounts, but the dc bias field can be easily varied over

hundreds of gauss. Thus in 1996, when we upgraded the original

BEC machine to incorporate the double-MOT technology, we

preserved the TOP trap coil design. Each is well suited to certain

types of experiments, as will be evident in the discussions below.

With the double-MOT setups we were able to routinely

make million-atom condensates in a highly reliable manner in both

TOP and baseball-type magnetic traps. These were used to carry

out a large number of experiments with condensates over the period

from 1996 to the present. Some of our favorite experiments are

briefly discussed below.

FAVORITE EXPERIMENTS

Collective excitations

In this section, by excitations we mean coherent fluctuations

in the density distribution. Excitation experiments in dilute-gas

BEC have been motivated by two main considerations. First, a

Bose-Einstein condensate is expected to be a superfluid, and a

superfluid is defined by its dynamical behavior. Studying excitations

is an obvious initial step toward understanding dynamical behavior.

Second, in experimental physics a precision measurement is almost

always a frequency measurement, and the easiest way to study an

effect with precision is to find an observable frequency that is

sensitive to that effect. In the case of dilute-gas BEC, the observed

frequency of standing-wave excitations in a condensate is a precise

test of our understanding of the effect of interactions.

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e radial 4 axial

FWHM (um)

5 10 15 20

time (ms)

FIG. 9. Zero-temperature excitation data from Jin et al. (1996). A weak m =

0 modulation of the magnetic trapping potential is applied to a 4500-atom

condensate in a 132-Hz (radial) trap. Afterward, the freely evolving response

of the condensate shows radial oscillations. Also observed is a sympathetic

response of the axial width, approximately 180° out of phase. The frequency of

the excitation is determined from a sine wave fit to the freely oscillating cloud

widths.

BEC excitations were first observed by Jason Ensher, Mike

Matthews, and then-postdoc Debbie Jin, using destructive imaging

of expanded clouds (Jin et al., 1996). The nearly zero-temperature

clouds were coherently excited (see below), then allowed to evolve

in the trap for some particular dwell time, and then rapidly

expanded and imaged via absorption imaging. By repeating the

procedure many times with varying dwell times, the time-

evolution of the condensate density profile can be mapped out.

From these data, frequencies and damping rates can be extracted.

In axially symmetric traps, excitations can be characterized by their

projection of angular momentum on the axis. The perturbation on

the density distribution caused by the excitation of lowest-lying

m = 0 and m — 2 modes cam be characterized as simple

oscillations in the condensate’s linear dimensions. Figure 9 shows the

widths of an oscillating condensate as a function of dwell time.

A frequency-selective method for driving the excitations is

to modulate the trapping potential at the frequency of the

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excitation to be excited (Jin ef al., 1996). Experimentally this is

accomplished by summing a small ac component onto the current in

the trapping magnets. In a TOP trap, it is convenient enough to

independently modulate the three second-order terms in the

transverse potential. By controlling the relative phase of these

modulations, one can impose m= 0, m = 2, or m = -2 symmetry on

the excitation drive.

There have been a very large number of theory papers

published on excitations; much of this work 1s reviewed by Dalfovo

et al. (1999). All the zero-temperature, small-amplitude excitation

experiments published to date have been very successfully modeled

theoretically. Quantitative agreement has been by and large very

good; small discrepancies can be accounted for by assuming

reasonable experimental imperfections with respect to the T = 0 and

small-amplitude requirements of theory.

The excitation measurements discussed above were then

revisited at nonzero temperature (Jin et al., 1997). The frequency of

the condensate excitations was clearly observed to depend on the

temperature, and the damping rates showed a strong temperature

dependence. This work is important because it bears on the little-

studied finite-temperature physics of interacting condensates.

Connection with theory (Hutchinson ef al., 1997; Dodd etal., 1998;

Fedichev and Shlyapnikov, 1998) remains somewhat tentative. The

damping rates, which are observed to be roughly linear in

temperature, have been explained in the context of Landau damping

(Liu, 1997; Fedichev ef al., 1998). The frequency shifts are difficult

to understand, in large part because the data so far have been

collected in a theoretically awkward, intermediate regime: the cloud

of non-condensate atoms is neither so thin as to have completely

negligible effect on the condensate, nor so thick as to be deeply in

the hydrodynamic (HD) regime. In this context, hydrodynamic

regime means that the classical mean free path in the thermal cloud

is much shorter than any of its physical dimensions. In the opposite

limit, the collisionless regime, there are conceptual difficulties with

describing the observed density fluctuations as collective modes.

Recent theoretical work suggests that good agreement with

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experiment may hinge on correctly including the role of the

excitation drive (Stoof, 2000; Jackson and Zaremba, 2002).

Two-component condensates

As mentioned above, the double-MOT system made it possible

to produce condensates even if one were quite sloppy with many of

the experimental parameters. One such parameter was the spin state

in which the atoms are optically pumped before being loaded into the

magnetic trap. As our student Chris Myatt was tinkering around

setting up the evaporation one day, he noticed, to his surprise, that

there seemed to be two different clouds of condensate in the trap.

They were roughly at the locations expected for the 2,2 and 1,-1 spin

states to sit, but that seemed impossible to us because these two states

could undergo spin-exchange collisions that would cause them to be

lost from the trap, and the spin- exchange collision cross sections

were thought to be enormous. After extensive further studies to try

and identify what strange spurious effect must be responsible for the

images of two condensate clouds we came to realize that they had to

be those two spin states. By a remarkable coincidence, the triplet and

singlet phase shifts are identical and so at ultralow temperatures the

spin-exchange collisions are suppressed in 87Rb by three to four

orders of magnitude! This suppression meant that the different

spin species could coexist and their mixtures could be studied. In

early work we showed that one could carry out sympathetic cooling

to make BEC by evaporating only one species and using it as a

cooling fluid to chill the second spin state (Myatt et al., 1997). We

also were able to see how the two condensates interacted and pushed

each other apart, excluding all but a small overlap in spite of the fact

that they were highly dilute gases.

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microwave ~6.8 GHz

—— F=1

1-1) ae rl

FIG. 10. Energy-level diagram for ground electronic state of *’Rb. The first

condensates were created in the 2,2 state. Mixtures containing the 2,2 and 1,-1

state were found to coexist. In later studies we created condensates in the 1,-1

state and then excited it to the 2,1 state using a microwave plus rf two- phonon

transition.

These early observations stimulated an extensive program of

research on two-component condensates. After Myatt’s original

measurements (Myatt ef al., 1997), our work in this field, led by

postdoc David Hall, concentrated on the 1,-1 and 2,+1 states (see

Fig. 10) because they could be coherently interconverted using two-

photon (microwave plus rf) transitions and they had nearly

identical magnetic moments and so saw nearly the same trapping

potentials (Matthews ef al., 1998). When the two-photon radiation

field is turned off, the rate of spontaneous interconversion between

the two spin species essentially vanishes, and moreover the optical

imaging process readily distinguishes one species from the other,

as their difference in energy (6.8 GHz) is very large compared to the

excited-state linewidth. In this situation, one may model the

condensate dynamics as though there were two distinct quantum

fluids in the trap. Small differences in scattering length make the two

fluids have a marginal tendency to separate spatially, at least in an

inhomogeneous potential, but the interspecies healing length is long

so that in the equilibrium configuration there is considerable overlap

between the two species (Hall ef al., 1998a, 1998b). On the other

hand, the presence of a near-resonant two-photon coupling drive

effectively brings the two energy levels quite close to one another: on

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resonance, the corresponding dressed energy levels are separated

only by the effective Rabi frequency for the two-photon drive. In

this limit, one may in a certain sense think of the condensate as

being described by a two-level, spinor field (Cornell e7 al., 1998;

Matthews efal., 1999b).

We got a lot of mileage out of this system and continue to

explore its properties today. One of the more dramatic experiments

we did in the two-level condensate was the creation, via a sort of

wave-function engineering, of a quantized vortex. In this

experiment we made use of both aspects of the two-level system—

the distinguishable fluids and the spinor gas. Starting with a near-

spherical ball of atoms, all in the lower spin state, we applied the

two-photon drive for about 100 ms. At the same time, we

illuminated the atoms with an off- resonant laser beam whose

intensity varied both in time and in space. The laser beam was

sufficiently far from resonance that by itself it did not cause the

condensate to transition from state to state, but the associated ac

Stark shift was large enough to affect the resonant properties of the

two-photon drive. The overall scheme is described by Matthews ez

al. (1999a) and Williams and Holland (1999). The net effect was to

leave the atoms near the center of the ball of atoms essentially

unperturbed, while converting the population in an equatorial belt

around the ball into the upper spin state. This conversion process

also imposed a winding in the quantum phase, from 0 around to two

pi, in such a way that by the time the drive was turned off, the upper-

spin-state atoms were in a vortex state, with a single quantum of

circulation (see Fig. 11). The central atoms were nonrotating and,

like the pimento in a stuffed olive, served only to mark the location

of the vortex core. The core atoms could in turn be selectively

blasted away, leaving the upper-state atoms in a bare vortex

configuration, whose dynamic properties were shown by postdoc

Brian Anderson and grad student Paul Haljan to be essentially the

same as those of the filled vortex (Anderson ef# a/., 2000).

Coherence and condensate decay

One of our favorite BEC experiments was simply to look at how a

condensate goes away (Burt ef al, 1997). The attraction of this

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experiment is its inherent simplicity combined with the far-reaching

implications of the results. Although it was well established that

condensates lived for a finite period, fractions of a second to many

seconds depending on conditions, no one had identified the actual

process by which atoms were being lost from the condensate. To

do this our co-workers Chris Myatt, Rich Ghrist, and Eric Burt

simply made condensates and carefully watched the number of atoms

and shape of the condensate as a function of time. From these data

we determined that the loss process varied with the cube of the

density, and hence must be three- body recombination. This was

rather what we had expected, but it was nice to have it confirmed.

In the process of this measurement we also determined the three-

body rate constant, and this was more interesting. Although three-

body rate constants still cannot be accurately calculated, it was

predicted long ago (Kagan ef al., 1985) that they should depend on

the coherence properties of the wave function. In a normal thermal

sample there are fluctuations and the three-body recombination

predominantly takes place at high-density fluctuations. If there is

higher-order coherence, however, as one has in macroscopically

occupied quantum states such as a single-mode laser, or as was

predicted to exist ina dilute gas BEC, there should be no such density

fluctuations. On this basis it was predicted that the three-body rate

constant in a Bose-Einstein condensate would be 3 factorial or 6

times lower than what it would be for the same atoms in a thermal

sample. It is amusing that such a relatively mundane collision

process can be used to probe the quantum correlations and

coherence in this fashion. After measuring the three-body rate

constant in the condensate we then repeated the measurement in a

very cold but uncondensed sample. The predicted factor of 6 (actually

74 + 2.6) was observed, thereby confirming the higher-order

concrence of BEC (Bure ai. 1997).

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0.0 0.5 1.0 es 2.0

azimuthal angle 0 (x)

FIG. 11. Condensate images showing the first BEC vortex and the measurement

of its phase as a function of azimuthal angle: (a) the density distribution of atoms

in the upper hyperfine state after atoms have been put in that state in a way that

forms a vortex; (b) the same state after a pi/2 pulse has been applied that

mixes upper and lower hyperfine states to give an interferogram reflecting the

phase distribution of the upper state; (c) residual condensate in the lower

hyperfine state from which the vortex was formed that interferes with a to give

the image shown in (b); (d) a color map of the phase difference reflected in (b);

(e) radial average at each angle around the ring in (d). The data are repeated

after the azimuthal angle 21T to better show the continuity around the ring. This

shows that the cloud shown in (a) has the 21T phase winding expected for a

quantum vortex with one unit of angular momentum. From Matthews ef al.,

1999a [Color].

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FIG. 12. Bosenova explosion from Roberts ef a/. (2001). From top to bottom these

images show the evolution of the cloud from 0.2 to 4.8 ms after the interaction

was made negative, triggering a collapse. On the left the explosion products are

visible as a blue glow expanding out of the center, leaving a small condensate

remnant that is unchanged at subsequent times. On the right is the same image

amplified by a factor of 3 to better show the 200 nK explosion products [Color]

Feshbach resonance physics

In 1992 Eric Cornell and Chris Monroe realized that dipole

collisions at ultralow temperatures might have interesting

dependencies on magnetic field, as discussed in the Appendix. With

this in mind we approached Boudwyn Verhaar about calculating the

magnetic-field dependencies of collisions between atoms in the

lower F spin states. When he did this calculation he discovered

(Tiesinga ef al., 1993) that there were dramatic resonances in all the

cross sections as a function of magnetic field that are now known as

Feshbach resonances because of their similarity to scattering

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resonances described by Herman Feshbach in nuclear collisions.

From the beginning Verhaar appreciated that these resonances would

allow one to tune the s-wave scattering length of the atoms and

thereby change both the elastic collision cross sections and the self-

interaction in a condensate, although this was several years before

condensates had been created. In 1992 we hoped that these

Feshbach resonances would give us a way to create enormous elastic

collision cross sections that would facilitate evaporative cooling.

With this in mind we attempted to find Feshbach resonances in the

elastic scattering of first cesium and then, with postdoc Nate

Newbury, rubidium. These experiments did provide us with elastic

scattering cross sections (Monroe ef al., 1993; Newbury ef al.,

1995), but were unable to locate the few-gauss-wide Feshbach

resonances in the thousand-gauss range spanned by _ then

theoretical uncertainty.

By 1997 the situation had dramatically changed, however. A

large amount of work on cold collisions, BEC properties, and

theoretical advances provided accurate values for the interaction

potentials, and so we were fairly confident that there was likely to

be a reasonably wide Feshbach resonance in rubidium 85 that was

within 20 or 30 gauss of 150 G. This was a quite convenient bias field

at which to operate our baseball magnetic trap, so we returned to the

Feshbach resonance in the hope that we could now use it to make a

Bose-Einstein condensate with adjustable interactions.

The time was clearly ripe for Feshbach resonance physics.

Within a year Ketterle (Inouye ef a/., 1998) saw a resonance in

sodium through enhanced loss of BEC, Dan Heinzen (Courteille e

al., 1998) detected a Feshbach resonance in photoassociation in

85Rb, we (Roberts ef al., 1998; notably students Jake Roberts and

Neil Claussen) detected the same resonance in the elastic scattering

cross section, and Chu (Vuletic ef al, 1999) detected Feshbach

resonances in cesium. Our expectations that it would be as easy or

easier to form BEC in *Rb as it was in *’RB and then use this

resonance to manipulate the condensate were sadly naive, however. Due

to enhancement of bad collisions by the Feshbach resonance, it was

far more difficult and could only be accomplished by following a

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complicated and precarious evaporation path. However, by finding the

correct path and cooling to 3 nK we were able to obtain pure *Rb

condensates of 16000 atoms (Roberts ef al., 2001).

The scattering length of these condensates could then be

readily adjusted by varying the magnetic field over a few gauss in

the vicinity of the Feshbach resonance (Cornish ef a/., 2000). This

has opened up a wide range of possible experiments, from studying

the instability of condensates when the self-interaction 1s sufficiently

attractive (negative a) to exploring the development of correlations

in the wave function as the interactions are made large and repulsive.

This regime provides one with a new way to probe such disparate

subjects as molecular Bose-Einstein condensates and the quantum

behavior of liquids, where there is a high degree of correlation. This

work represents some of the most recent BEC experiments, but

almost everything we have explored with this system has shown

dramatic and unexpected results. Thus it is clear that we are far from

exhausting the full range of interesting experiments that are yet to

be carried out with BEC.

In the first of these Feshbach resonance experiments our

students Jake Roberts, Neil Claussen, and postdoc Simon Cornish

suddenly changed the magnetic field to make a negative. We

observed that, as expected, the condensate became unstable and

collapsed, losing a large number of atoms (Roberts ef al, 2001).

The dynamics of the collapse process were quite remarkable. The

condensate was observed to shrink slightly and then undergo an

explosion in which a substantial fraction of the atoms were blown

off (Donley, 2001). A large fraction of the atoms also simply

vanished, presumably turning into undetectable molecules or very

energetic atoms, and finally a small cold stable remnant was left

behind after the completion of the collapse. This process is

illustrated in Fig. 12. Because of its resemblance (on a vastly lower

energy scale) to a core collapse supernova, we have named this the

Bosenova. There is now considerable theoretical effort to model this

process and progress is being made. However, as yet there is no clear

explanation of the energy and anisotropy of the atoms in the

explosion, the fraction of vanished atoms, and the size of the cold

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remnant. One of the more puzzling aspects is that the cold remnant

can be far larger than the condensate stability condition that

determines the collapse point would seem to allow (Donley, 2001).

Another very intriguing result of Feshbach resonance studies

in Rb was observed when our students Neil Claussen and Sarah

Thompson and postdoc Elizabeth Donley quickly jumped the

magnetic field close to the resonance while keeping the scattering

length positive. They found that they could observe the sample

oscillate back and forth between being an atomic and a molecular

condensate as a function of time after the sudden perturbation

(Donley eft al., 2002). This curious system of a quantum

superposition of two chemically distinct species will no doubt be a

subject of considerable future study.

An optimistic appendix

Until a new technology comes along to replace evaporative

cooling, the crucial issue in creating BEC with a new atom is

collisions. In practice, this means that planning a BEC experiment

with a new atom requires learning to cope with ignorance. It is easy

to forget that essentially nothing is known about the ultralow-

temperature collisional properties of any atomic or molecular

species that 1s not an atom in the first row of the Periodic Table. One

cannot expect theorists to relieve one’s ignorance. Interatomic

potentials derived from room-temperature spectroscopy are

generally not adequate to allow theoretical calculations of cold

elastic and inelastic collision rates, even at the order-of- magnitude

level. Although the cold collisional properties of a new atom can

be determined, this is a major endeavor, and in most cases it is

easier to discover whether evaporation will work by simply trying

iW.

Launching into such a major new project without any

assurances of success is a daunting prospect, but we believe that, if

one works hard enough, the probability that any given species can be

evaporatively cooled to the point of BEC is actually quite high. The

scaling arguments presented below in support of this assertion are

largely the same as those that originally encouraged us to pursue

Winter 2016

BEC in alkalis, although with a bit more refinement provided by age

and experience.

Although there is an extensive literature now on evaporative

cooling, the basic requirement is simply that there be on the order of

100 elastic collisions per atom per lifetime of the atoms in the trap.

Since the lifetime of the atoms in the trap is usually limited by

collisions, the requirement can be restated: the rate of elastic

collisions must be about two orders of magnitude higher than the

rate of bad collisions. As mentioned above, there are three bad

collisional processes, and these each have different dependencies on

atomic density in the trap, m: background collisions (independent of

n), two- body dipolar relaxation (am), and three-body recombination

(an*). The rate for elastic collisions is nov, where n is the mean

density, 6 1s the zero-energy s-wave cross section, and v is the mean

relative velocity. The requirement of 100 elastic-to-inelastic collisions

must not only be satisfied immediately after the atoms are loaded into

the trap, but also as evaporation proceeds toward larger m and smaller

v. With respect to evaporating rubidium 87 or the lower hyperfine

level of sodium 23, Nature has been kind. One need only arrange for

the initial trapped cloud to have sufficiently large n, and design a

sufficiently low-pressure vacuum chamber, and evaporation works.

The main point of this section, however, is that evaporation is likely

to be possible even with less favorable collision properties.

Considering the trap loss processes in order, first examine

background loss. Trap lifetimes well in excess of what are needed for

‘’Rb and Na have been achieved with standard vacuum technology.

For example, we now have magnetic trap lifetimes of nearly 1000 s.

(This was a requirement to achieve BEC in *’/Rb with its less favorable

collisions.) If one is willing to accept the added complications of a

cryogenic vacuum system, essentially infinite lifetimes are possible. If

the background trap loss is low enough to allow evaporative cooling

to begin, it will never be a problem at later stages of evaporation

because nv increases.

If dipolar relaxation is to be a problem, it will likely be late

in the evaporative process when the density is high and velocity

low. There is no easy solution to a large dipolar relaxation rate in

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terms of changing the spring constant of the trap or the pressure of the

vacuum chamber. Fortunately, one is not required to accept the value

of dipolar collisions that Nature provides. In fact, all one really has

to do is operate the trap with a very low magnetic bias field in a

magnetic trap, or if one uses an optical trap very far off-resonance

(such as CO? laser), trap the atoms in the lowest spin state, for

which there are no dipole collisions. The bias field dependence comes

about because below a field of roughly 5 G, the dipolar rate in the

lower hyperfine level drops rapidly to zero. This behavior is simple to

understand. At low temperature, the incoming collisional channel must

be purely s wave. Dipolar relaxation changes the projection of spin

angular momentum, so to conserve angular momentum the outgoing

collisional channel must be d wave or higher. The nonzero outgoing

angular momentum means that there is an angular momentum barrier

in the effective molecular potential, a barrier of a few hundred

microkelvin. If the atoms are trapped in the lower hyperfine state

(F=1, mr=-1, in rubidium 87) the outgoing energy from a dipolar

collision is only the Zeeman energy in the trapping fields, and for B

less than about 5 G this energy is insufficient to get the atoms back

out over the angular momentum barrier. If relaxation is to occur, it

can happen only at interatomic radii larger than the outer turning point

of the angular momentum barrier. For smaller and smaller fields, the

barrier gets pushed further out, with correspondingly lower transition

rates.

It is unlikely that the three-body recombination rate

constant could ever be so large that three-body recombination

would be a problem when the atoms are first loaded from a MOT

into the evaporation trap. As evaporation proceeds, however, just

as for the dipolar collisions, it becomes an increasingly serious

concern. Because of its density dependence, however, it can

always be avoided by manipulating the trapping potential.

Adiabatically reducing the trap confinement has no effect on the

phase-space density but it reduces both the density and the atom

velocity. The ratio of three-body to elastic collisions scales as |/ny.

Therefore, as long as one can continue to turn down the confining

strength of one’s trap, one can ensure that three-body

Winter 2016

recombination will not prevent evaporative cooling all the way

down to the BEC transition.

To summarize, given (i) a modestly flexible magnetic trap,

(ii) an arbitrarily good vacuum, (iii) a true ground state with F #.

0, and (iv) non-pathological collisional properties, almost any

magnetically trappable species can be successfully evaporated to

BEC. If one is using a very far off-resonance optical trap (such as a

CO2 dipole trap) one can extend these arguments to atoms that

cannot be magnetically trapped. In that case, however, current

technology makes it more difficult to optimize the evaporation

conditions than in magnetic traps, and the requirement to turn the

trap down sufficiently to avoid a large three-body recombination

rate can be more difficult. Nevertheless, one can plausibly look

forward to BEC in a wide variety of atoms and molecules in the

hubuire:

Acknowledgments

We acknowledge support from the National Science

Foundation, the Office of Naval Research, and the National Institute

of Standards and Technology. We have benefited enormously from

the hard work and intellectual stimulation of our many students

and postdocs. They include Brian Anderson, Mike Anderson, Steve

Bennett, Eric Burt, Neil Claussen, Ian Coddington, Kristan Corwin,

Liz, Donley, Peter Engels, Jason Ensher; David Hall, Debbie Jin,

Tetsuo Kishimoto, Heather Lewandowski, Mike Matthews, Jeff

McGuirk, Chris Moroe, Chris Myatt, Nate Newbury, Scott Papp,

Cindy Regal, Mike Renn, Jake Roberts, Peter Schwindt, David

Sesko, Michelle Stephens, William Swann, Sarah Thompson, Thad

Walker, Yingju Wang, Richard Watts, Chris Wood, and Josh Zirbel.

We also have had help from many other JILA faculty, including

John Bohn, Chris Greene, and Murray Holland.

Washington Academy of Sciences

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Washington Academy of Sciences

10]

Defining and Measuring Optical Frequencies‘

— the Optical Clock Opportunity — and More -

John L. Hall

JILA, NIST, and University of Colorado

Abstract

Four long-running currents in laser technology met and merged in 1999-2000.

Two of these were the quest toward a stable repetitive sequence of ever-shorter

optical pulses and, on the other hand, the quest for the most time-stable,

unvarying optical frequency possible. The marriage of UltraFast- and

UltraStable lasers was brokered mainly by two international teams and became

exciting when a special “designer” microstructure optical fiber was shown to

be nonlinear enough to produce “white light” from the femtosecond laser

pulses, such that the output spectrum embraced a full optical octave. Then, for

the first time, one could realize an optical frequency interval equal to the

comb’s lowest frequency, and count out this interval as a multiple of the

repetition rate of the femtosecond pulse laser. This “gear-box” connection

between the radio frequency standard and any/all optical frequency standards

came just as Sensitivity-Enhancing ideas were maturing. The four-way Union

empowered an explosion of accurate frequency measurement results in the

standards field and prepares the way for refined tests of some of our cherished

physical principles, such as the time-stability of some of the basic numbers in

physics (e.g., the “fine-structure” constant, the speed of light, certain atomic

mass ratios ...), and the equivalence of time-keeping by clocks based on

different physics. The stable laser technology also allows time-

synchronization between two independent femto-second lasers so exact they

can be made to appear as if the source were a single laser. By improving

pump/probe experiments, one important application will be in bond-specific

spatial scanning of biological samples. This next decade in optical physics

should be a blast!

Overview and Summary

THE VIEW BACKWARD over some momentous developments often suggests

a kind of certainty and inevitability that may not have been evident, even in

the slightest form, when the story was going on. One modern trend is to

focus on some particular research project — one which is so simple and

transparent that the Manager can expect to be successful in the chosen

| The 2005 Nobel Prize for Physics was shared by Roy J. Glauber, John L. Hall, and Theodor W.

Hiansch. This lecture is the text of Dr. Hall’s address on the occasion of the award. Reprinted

from RevModPhys.78.1279.

Winter 2016

102

research task. But such a project will likely have modest consequences:

Surely its consequences were at least dimly visible from the beginning. By

contrast, this “Optical Frequency Comb” capability has come “out of the

blue” from a remarkable synthesis of independent “state-of-the-art”

developments in four distinct fields: UltraStable Lasers, UltraFast Pulse

Lasers, Ultra-NonLinear Materials and Responses, and UltraSensitive Laser

Spectroscopy. These separate fields were alike in their shared — but

independent — pursuit of advancing simple and effective technology for

using electromagnetic signals for their own spectroscopic and other optical

physics interests in the visible domain. After the Great Laser Technology

Synthesis of 1999-2000, celebrated by the brief name of “Optical Frequency

Comb,” the Optical Toolbox has really blossomed. In respecting our Patron,

Dr. Nobel, we may be more expansive and clear: the field of optics has

blossomed explosively!

The resulting new capabilities are unbelievably rich in terms of the

tools and capabilities that have been created, and these in turn are

reinforcing progress in these related contributing fields. For example, after

the frenzy of the first generation frequency measurements, some of the

Generation II comb applications now include: low-jitter time

synchronization between ultrafast laser sources, coherent stitching-together

of the spectra of separate fs laser sources so as to spectrally broaden and

temporally shorten the composite pulse, optical waveform synthesis for

Coherent Control experiments, precision measurement of optical

nonlinearities using the phase measurement sensitivity of rf techniques,

coherently storing a few hundred sequential pulses and then extracting their

combined energy to generate correspondingly more intense pulses at a

lower repetition rate... . Attractive topics of research for Generation III

applications include precise remote synchronization of accelerator cavity

fields and the stable reference oscillators for Large Array Microwave

Telescopes; and potential reduction of the relative phase-noise of the

oscillator references used for deep space telescopes. (NASA, VLBI ...)

That’s just part of the first five years.

So in the precision metrology field, what exactly could one say is

different now? In the same way we have enjoyed for the last half-century

powerful spectroscopy methods with radiofrequency signals (consider

Magnetic Resonance Imaging as one of its useful forms!), we now can use

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frequency-control methods for optical spectroscopy. But there is a really

important difference: the number of cycles per second in the optical domain

is roughly 10-million-fold greater than in the rf domain, even as the rf

processes themselves are still a few million-fold faster than human

perception scales. In essence, these large factors map into a corresponding

improvement in resolution — our measurement capability. See the discussion

below. With human senses we can perceive halves and quarters and tenths,

and perhaps a little better. These capabilities are enhanced approximately

by the product of these two large numbers, bringing us immediately into the

garden of a few parts in 10'* metrology. We can do even better by averaging

independent measurements.

Metrological Standards and Science

A Close and bi-directional Connection

On occasion, accumulation of progress in the details of some

scientific enquiry leads us to a glorious new vision of some parts of our

experience: basically a new insight or organizing principle becomes

available. But behind this revelation normally is a huge amount of

painstaking work, quantitatively stating experimental results, which

normally are expressed in absolute units. Sometimes an experiment can

provide its own internal calibration, but in the main we really need to have

practical standards to reference the measurements against. Of course the

Standards must themselves be reproduced and distributed before the

scientific results can be confirmed by several labs. The best case 1s that the

needed Standard is based on some fundamental physical effect, ideally a

quantum effect, so it can be independently realized by different laboratories

at the same accuracy. This standards-realization process 1s in a revolution

itself! [1]

The Length Standard and its Relationship to Frequency/Time

It’s useful to discuss a bit about metrological Standards, which we

can initially take to be the seven base quantities of the Systéme International

d'Unités (International System of Units), or more briefly the SI, or “the

Metric System” These are Mass, kg; Time, s; Length, m; Current, A;

Temperature, K; Quantity of Matter, mol; Unity of Light Intensity

(Candela), cd.. From these seven base units, another ~30 useful derived

units can be defined. For our purposes of stretching measurement precision

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to the ultimate limits, clearly Time and Length are the two quantities

offering the highest potential precision. For eons the day was a natural unit

for Time, but standards for Length have seemed artificial and arbitrary. In

1791 the Metric System was first discussed but, lacking serious metrology

experience, these Age of Enlightenment gentlemen of the French Academy

of Sciences decided that the Metre would be defined as some small fraction

(“4 x 10°’) of the Earth’s circumference on a great circle passing through

the poles and France. Of course, having the standard based on surveying

had some limitations in practical lab work, but at least the unit of length was

finally a definite and basically absolute distance. This was welcome change

since public exhibits in places such as Braunschweig, Germany and on

Santorini Island, Greece show there was a succession of length standards in

sequential use, as a new Duke of different personal arm length came into

power. But by 1875, with the Treaty of the Metre Convention, a stable metal

bar began to look like a good idea. While not fully universal and

independently realizable, the factory could make many of these prototype

Metre bars, and could confirm their equivalence.

The community of Metric countries in 1889 welcomed the improved

X-cross-section meter bars known as the “International Prototype Metre”

length standard. This design used graduations (lines) engraved onto a

platinum-iridium bar, with a Meter defined as the separation between two

graduation lines at 0 C, measured with a specified mounting arrangement,

and under atmospheric pressure. The 30 new bars were calibrated using an

optical comparator technique, before dissemination of two to each country.

By 1890 A. A. Michelson had identified the exceptional coherence

of the Cd red line, and by 1892 had used it with his new interferometer to

determine the length of the International Prototype Metre. His

measurements showed the defined Metre contained 1,553,164.13 units of

the wavelength of the cadmium red line, measured in air at 760 mm of

atmospheric pressure at 1S C. For this and other contributions, Michelson

was awarded the Nobel Prize in 1907. Of course thermal expansion was a

limiting problem, such that when the low-expansion steel alloy Jnvar was

invented, the creator (and Director of the BIPM), C. D. Guillaume, was

awarded the Nobel Prize for 1920. However, the SI Metre definition was

unchanged for 85 years: the Meter Bars worked well and optical

comparators got fatigueless photo-electric eyes.

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Spectroscopic experiments and supporting Quantum Theory led to

improved understanding and improved light sources. The metrological

needs of the World Wars changed the Science climate, and transportation

disruptions emphasized the advantage of having independently-

reproducible standards based on quantum physics. Eventually, in 1960 the

Eleventh General Conference on Weights and Measures was able to

redefine the International Standard of Length as 1,650,763.73 vacuum

wavelengths of orange light resulting from transitions between specified

atomic energy levels of the krypton isotope of atomic weight of 86. Going

forward with a new definition, one would say the Kr wavelength is A = 1 m

/ 1,650,763.73 = 0.605,780,211 um. While the adopted Definition speaks

about unperturbed atoms, in fact several shifts were observed in light from

the discharge lamp used for realizing this Metre in practice. Pressure shifts

and discharge operating conditions were stabilized by operating the lamp at

a specified discharge current and at a fixed pressure and temperature (using

the triple-point of liquid nitrogen). A field-induced gas flow of Kr’ led to a

wavelength difference of light viewed from the two cell ends. When laser

comparisons with this standard were performed, the additional problem of

radially-dependent Doppler shifts of the emitted light was discovered.

The 1960’s and 1970’s saw a number of different stabilized lasers

systems introduced, refined, and the wavelengths measured and compared

between various national labs. Basically, all these laser systems were

entered into the competition to be the next International Length Standard.

There were then 48 nations involved 1n the Metre Convention, so politically

speaking, choosing one out of the many offered candidate lasers would be

difficult. In addition, none of these approaches were overwhelmingly

superior, when performance, cost and complexity were all considered. And

scientifically, it seemed attractive for the new Length Standard definition to

be based on the Speed of Light, introduced as a defined quantity. On the

basis of a number of laser-based measurements, this value was taken as

299,792,458 m/s exactly, a rounded value in accord with the measurements

of the several standards labs. This redefinition of 1983 took the form:

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“the Meter is the length of the path traveled by light in vacuum during a

time interval of 1/299, 792,458 of a second. The speed of light is

c = 299,792,458 m/s, exactly.

The second is determined to an uncertainty, U = 1 part in 10'* by the

Cesium clock.”

The General Conference also suggested several recommended radiations for

realizing the meter at that time, e.g.: “The wavelength of the 1odine-

stabilized Helium-Neon laser is

AHeNe = 632.99139822 nm ,

with an estimated relative standard uncertainty (U) of + 2.5 x 101'.”

In all of these changes in definition, the goal was not only to improve the

precision of the definition, but also to change its actual length as little as

possible. See [3]. With the speed of light defined, an optical frequency

(linked to time) can thus serve as a length unit.

Fundamental Physics Issues in the Re-Definition of Length

At the times of these redefinitions, there were some concerns that

we were switching the physical basis for the Metre definition. For example,

if in the future we discover that some of the “constants of Physics” actually

are Slowly changing, one could worry that the new definition might impact

or even limit our discovery process. In any case, we would be unaware of a

global change that would conserve the physical relationships we have

discovered. But could there be a differential effect that might be observable?

Before 1960 we were accepting the spacing of some lattice planes in the Pt-

Ir alloy of the Meter Bar as our measurement basis for length: this length

certainly would fundamentally involve Quantum Mechanics, and Electricity

and Magnetism. And, considering the thermal vibration of molecules in the

somewhat-anharmonic interatomic potentials, we can suppose that the

nuclear masses — and thus the Strong Interactions — will also play a role in

length via the thermal expansion. With the 1960 redefinition of the Metre

in terms of a Krypton atom’s radiation’s wavelength, perhaps we were

opening some opportunity for confusion? Now Quantum Mechanics and

Electricity and Magnetism are still fundamentally involved, but the atom’s

mass is involved only in a reduced-mass correction, rather than via thermal

effects. Certainly a new “constant,” the speed of light, is linearly serving as

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the dimensioned scale constant. Initially the 1983 redefinition appears to be

still a different sort compared with the 1960 Kr definition, but really it just

repeats the energy level difference idea (now it is Cs in defining the second

rather than Kr defining an optical energy) followed by a conversion of

dimensions. Who knows if there is some fun hidden in here?

Where we have come to is that the SI is now functioning with six,

rather than seven, basic units. The Metre has been demoted to a derived unit,

and the significance of Time and Frequency have been further elevated.

This begins a long story, with the SI base units being challenged by

spectacular advances “at the bottom of a Dewar” [4], giving us a Josephson-

effect based voltage standard (Nobel Prize of 1973), while the von-K litzing-

effect defines a quantum resistance standard (Nobel Prize 1985). Taken

together as V’/R, an electrical Watt unit is apparent, while an SI Watt —

defined as a Joule per second — would be represented as 2 kg (m/s)? /s. The

relationship between these is established by a “Watt Balance” experiment

[5]. Recently the Single Electron Transistor begins to enable digital

counting of electron charges per second, contacting the SI Ampere, the unit

of electric current. This interface between metrology and quantum physics

is becoming a “Hot Topic” of our time [1, 6]. The remarkable advances in

Metrology also allow — and advances in Cosmology and Astronomy

strongly motivate — curiosity about the “exactness” and “time-invariance”

of the various physics numbers used in our description of physical reality.

Clocks and Time

Time represents our most precisely measurable quantity and so it

always has attracted certain kinds of devoted researchers. But also, now

with various sensors and microprocessor control, many physical parameters

can be read out by frequency measurements, and so we add a huge number

of scientists in other fields who want to recover the finest details within their

measurements. (Still, many really important research subjects are not yet so

well developed that these frequency tools are useful: for example, world-

changing decisions about air pollution management are being made even

though we scarcely are sure about the sign of some effects.)

But for technology people, the improvement of time measurement

precision grows as a field of intense interest and competition worldwide. In

no small part this is because of the very advances singled out by this year’s

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Prize: a capability jump by several decades is uncommon in any field, let

alone the field where the precision of measurement was already at the

highest level, and had already been driven to near its apparently basic limits.

Of course interest in time has been part of man's history from our

beginnings, but only in the last several recent centuries have some lucky

subsets of people been somewhat isolated from seasonal variations, with

leisure to think about Nature, and so time as an experimental parameter

began to emerge. Nowadays we can look from the scientific and

experimental point at the question: why would one be interested in time?

For those who love precision, the clear reason is that time is the most

powerful metrological variable.

Scaling of Precision Attainable when we are Measuring Time

The precision of time measurements can be increased essentially

without limit, by increasing the measurement duration and simply counting

the increased number of cycles of some regularly-spaced events. However

a stronger information growth with measurement duration is possible if we

have a nice source that has coherence from the beginning of the

measurement until the end. (For the present purpose we may take this

“coherence” to mean that if we know the oscillation cycle’s phase early in

the measurement, the coherent source 1s so steady that the oscillation phase

could be predicted at later times near the measurement’s end to a precision

of | radian of phase.) In this case we can have a measurement precision

which will grow with the measurement interval t according to t*”. A simple

way to explain this assertion is to suppose we divided the measurement

duration into 3 equal sections, each with N/3 measurements. In the starting

zone we compare the reference clock and the unknown clock, with a relative

phase precision which scales as (N/3)'”. Next, in the middle section, we

merely note the number of events, N/3. In the last section we again estimate

the analog phase relationship between test and reference waves, with a

relative imprecision which is again (N/3)'. Subtracting the two analog

phases increases the uncertainty of one measurement by a factor 2!” so,

altogether, the relative precision increases as (1/2'”) x (N/3)°”. Thinking of

a microwave frequency measurement, with a base frequency of 10!° Hz, in

a 1 s measurement we have a factor of 10° potentially to win. Commercial

counters already can register 12 digits in 1 s for a reasonable input signal.

One can see there is just a huge gain in measurement precision if we can

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measure a coherent frequency source in a proper way: No wonder we have

the situation where metrology scientists as well as philosophers, sailors, and

farmers are interested in clocks and time and seasons [7]. Indeed our most

powerful test of the existence of Einstein’s predicted gravitational radiation

comes from the observed shortening of the year of the Hulse-Taylor binary

pulsar: orbital clock physics vs. quantum frequency standard physics on the

earth. This marvelous work was celebrated by the Nobel Prize of 1993.

What makes a clock?

The three essentials of clocks are: a source of regular events, a

counter/integrator to totalize the events, and a suitable readout mechanism

to present the current result to an interested human or machine. In many

ways the frequency source is the most interesting part since it is intrinsically

an analog system, where the design goal is to diminish as little as possible

the intrinsic stability of some physical oscillation, in the course of reading

out its information. In this game, nuance and subtlety count for a lot. It is

customary that the performance of clocks based on some well-known source

of regular “clicks” will be improved several orders of magnitude by the

work of many people over many years, with the ultimate fate of becoming

suddenly obsolete due to the introduction of a better kind of stable oscillator.

The new idea must be a serious advance, since it must be competitive at the

start of its life with the previous technology which has been enhanced and

improved in many stages. Still, some technologies have had a long lifetime

— for example one can still buy a good wristwatch based on a torsional

oscillator, even though this balance wheel concept was used by Ch.

Huygens in 1675.

Keeping time has been of serious interest since man turned agrarian,

but became of critical interest with the expansion of lucrative international

trade: “inevitable” shipwrecks could be avoided by better knowledge of

position (mainly longitude) at sea. Parliament’s Longitude Prize of 1714

(above $10 M in current terms) attracted John Harrison's attention and some

40 years of his inventive work. In 1761 his H-4 clock demonstrated 1/5 s/d,

dv/v ~2.5 x10° even while at sea. This was several-fold better that the

requirement, but only half the Prize was initially paid: in part the

controversy was about the Intellectual Property! A second problem was

conflict of interest within the judging Committee. (This story is well-told in

[7].) Present customers of precise timekeeping include TV Networks (for

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synchronization), cellular telephone companies, the GPS users who need

the limiting performance, radio astronomers, NASA Deep Space Tracking,

and various other branches of Science in which a physical variable has been

read out by frequency methods.

Evolution of Frequency Sources: Distinguishing Precision and Accuracy

In discussing the performance of a mechanical clock, or the

electronic oscillators based on vibrational modes of quartz crystals, it is

clear that the basic frequency is set by mechanical dimensions. Such a

device could be stable and have good precision, in that its readout could be

determined with many digits, but there can be no claim to any particular

fixed or natural frequency. Still the stability of any particular crystal device

could be remarkable: a drift of >10°° /day gradually improved to the present

<~] x10°!°/day, while the shift with acceleration remains near 10° per “g”.

The high frequency of electronic oscillators served well for convenient

interpolation between “clicks” of the absolute standard, provided by zenith

sightings of the daily motion of the Sun, as codified by the 1875 Metre

Convention. (Later the Earth rotation data series were based on telescopic

observations of the lunar occultation starts of various stars and planets.) By

the 1950’s the electronic oscillators were refined enough that variability

~10°° was inferred in the earth’s spin rate, and was associated with changes

of the earth-atmosphere system’s moment of inertia due to North-South

ocean tides, and large storms. The community wished to eliminate the

variability, but still needed an absolute and universal (rather than local

artifact) standard. The new choice in 1960 adopted a stated number of

seconds in the “Tropical Astronomical Year 1900”. Perhaps this was good

in its motivation, 1n that the rotation of the earth around the sun would have

a lower level of perturbation. However a clock/oscillator that has only a

single click per year will be hard to enjoy at its full precision. As a

metrology principle we rather would prefer the basic frequency source to be

at a very high frequency so that the integer multiple of the standard’s clicks

will be a huge digital number in our measurement of some interesting

phenomenon, and the unavoidable noise and uncertainty of the remaining

analog subdivision of the unit will be as insignificant as possible.

Washington Academy of Sciences

Electronic Clocks based on Quantum Transitions

Based on Otto Stern’s atomic beam method, which had resulted in

his Nobel Prize of 1943, I. I. Rabi introduced atomic beam resonance

methods which allowed probing internal (hyperfine) quantum energy states

of atoms such as Cesium with greater precision. This work was recognized

by the Nobel Prize of 1944. Using atoms in this way, the independent

realizability and universality requirements for a Primary Standard could be

well addressed. In addition, the transition frequencies were near the high-

frequency-end of the usable rf spectrum, so the Metrology aspects were

optimized as well. The first Atomic Beam Clock was developed at NBS in

1949 based on microwave transitions in Ammonia, and by 1955 Cs beam

clocks were in operation at the NPL and NBS. The powerful Method of

Separated Oscillating Fields was invented by N. F. Ramsey, reported in

1955, and later recognized by the Prize in 1989. In this dual-excitation

concept, suitable atoms were excited once, and then left to evolve their

internal phase (ideally) free of perturbation, until a second excitation pulse

effectively completed the interferometric comparison of the phase evolution

rates between the atomic and laboratory oscillating systems. Progress on the

Cs beam atomic frequency standard was widespread and rapid, allowing

redefinition in 1967 of the SI Second as 9 192 631 770 units of the Cs

hyperfine oscillation period. Correspondingly, the Cs oscillation frequency

is defined as (exactly) 9 192 631 770 Hertz (cycles of per second). The

specialists involved in this redefinition of Time and Frequency wisely did

not specify exact details of the measurement process, leaving room for

considerable progress. For example when laser-based optical pumping of

atoms between hyperfine states became feasible and popular in the early

1990’s, NIST colleagues built a new atomic beam cesium standard, NIST-

7, based on optically transferring most of the population from the 16

available hyperfine levels into the special ( |3,0> ) lower state involved in

the clock transition. Along with this factor, ~16x, improvements of the atom

source itself, and better frequency source and readout electronics were

helpful. Above all, computer-based signal processing and active control of

measurement systematic offsets made it possible to reduce the inaccuracy

of realizing the Cs second at NIST to ~5 x10°'°. But as usual in the art-form

of Precision Measurement, this “tour de force” system was soon made

obsolete in a single step by a qualitatively better technology.

Winter 2016

As shown by Kasevich and Chu [8], laser cooling of the Cs atoms

made it possible to successfully implement the “atomic fountain” concept

for the realization of the Cs-based frequency definition. By shifting laser

frequencies or powers, a slowly moving ball of atoms could be dispatched

vertically upward through the excitation rf cavity, reaching apogee a good

part of a meter above the cavity, and then beginning the return trip to pass

through the excitation cavity a few 100 ms later. With such a long coherent

interaction time, instantly the resonance linewidth dropped to ~ 1 Hz, down

from ~300 Hz in the previous epoch of thermal beam of atoms. Optical

probing of the atoms below (and temporally after) the cavity could yield the

excitation-probability vs. probe-frequency-tuning curve needed to control

the source oscillator’s frequency. By using suitably-closed optical

transitions for readout, one can have many photons emitted per atom so that,

even after solid angle and detection inefficiencies are considered, the

measurement noise is not much larger than the minimum associated with

the finite number of atoms. Andre Clairon and his colleagues made the first

real Cs Fountain Frequency Standard, in 1995 [9] at the Paris Institute now

known as LNE-SYRTE (Laboratoire National de Métrologie et d'Essais —

Systemes de Références Temps/Espace). Even without the contemporary

schemes to break this atom-shot-noise limit, the fountain Cs clocks at NIST

and SYRTE now achieve accuracy levels below 1 x10°'° when all the known

measurement and perturbation issues are taken into account [10]. Of course

with the resolution improvement one hopes for more potential accuracy, but

will have beforehand an expanded list of small shifts and niggling concerns

to consider. After all, even with the extended interaction time, fewer than

10'° oscillation cycles are counted, so the achieved inaccuracy of 1 x10"!

already corresponds to 10 ppm splitting of the atomic fountain’s resonance

linewidth. Fountain Cs clocks are limited by two newly important effects,

collisionally induced frequency shifts due to the hugely increased atom

density [11], and shifts due to the effects of the ambient thermal radiation

associated with the vacuum system’s walls. Attempting to split lines further

always brings a diverging list of new small problems, leading to an effective

barrier.

An important observation is that for many types of Quantum

Absorber samples the line broadening processes will be the same for both

radio and optical frequency domains. For example, the atomic fountain

apparatus could explore optical transitions, rather than microwave ones,

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with the same interaction time. Clearly we would prefer the higher base

frequency of the optical world, since the resonance feature of interest will

then display a relative sharpness increased by roughly the same huge factor

of optical/microwave frequency ratio. With sharper line shapes we can

expect more precise measurements that will let us better see the small

effects of various experimental parameters, leading to better independent

reproducibility which, with major investment of efforts, can often be

parlayed into nearly a corresponding increase in measurement accuracy

capability as we come more fully to characterize the offset processes. But

before the Millennium Year of the Optical Comb, just how did you plan to

measure the absolute optical frequency?

This repeatability idea seems weaker than the gold standard of

accuracy, which additionally conveys our being able to connect the

measured result with the base units of the Systeme International. But in fact

we now know several optical clock systems that have 10-fold smaller

uncertainty than the Cs standard. So before a redefinition is appropriate,

their comparisons will be most interesting, especially as an entry point for

one of the most interesting branches of Science, trying to figure out which

physical “laws” are essentially exact, which ones are ignoring some details

to have a tidy presentation, and which are in fact stating “facts” about

Nature which are not exactly actually true. Celestial mechanics, ideal gas

laws ignoring molecular volumes, and parity conservation in atomic physics

could be my examples.

Starting the Dream of Optically-based Clocks

The Laser Arrives

The future of metrology was changed fundamentally on 12

December 1960 when a small team at Bell Labs, led by Ali Javan,

eventually found the right conditions for their Optical Maser to generate

self-sustained optical oscillations. Their specially crafted gas discharge tube

had the improbable situation in which the populations in two particular

Neon atomic levels were reversed from the thermal norm: by means of the

discharge in the more-abundant He gas, collisional energy transfer set up a

population inversion, whereby more atoms were in the Ne’s higher energy

state. It is impressive that these conditions were established on the basis of

careful measurements and modeling of the discharge conditions! Having the

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populations inverted from the usual case reverses the sign of the absorption

that experience teaches us is a universal property of (normal) matter.

Accordingly, with an inverted population, rather than absorption, Javan’s

group had optical emission. The atoms would provide amplification of any

resonant optical signal passing down the discharge cell. A few percent gain

wouldn’t be very exciting normally, except that the utilized multilayer

mirrors were designed and fabricated to have reflection losses that could be

even smaller, setting the stage for a buildup of power on every pass. So

finally they did obtain a self-sustained continuous optical oscillation, and

observed the collimated beam that was anticipated by Charles Townes and

Arthur Schawlow in a classic paper of 1958. Similar ideas were also

considered in the Former Soviet Union, leading to the Nobel Prize of 1964

being shared by N. Basov, A. Prokhorov, and Townes.

Connection to Glauber’s Coherent States of Light

In planning a theoretical study of optical fields, perhaps one can

understand starting with known results for single-photon fields, then adding

a few photons cautiously to see what happens. Actually, for all of us

following Professor Glauber’s work it was surprising just how few photons

were needed for the new photon density distribution functions to change

fundamentally from the customary Poisson limit: with increasing number

of photons in a mode the fields start showing the small fractional

fluctuations that would characterize a classical field. On the experimental

side, for Javan’s very first laser, the output laser power was ~ | milliWatt,

about 10!° photons per second! We can proceed to estimate the expected

fractional variation of 1/ JN , but with such an incredibly large number of

coherent photons in one mode, the result 1s an unphysically small variation.

Thousands of merely technical processes would cause fluctuations larger

than the predicted 1:10°! An equivalent statement is that these lasers were

operating strongly, far into the domain of classical fields, and quantum

fluctuations would be very hard to observe. Indeed it was not until the end

of the 1970’s that people began again to appreciate how to study manifestly

quantum fields with just a few photons in them. At this vastly-reduced

intensity, quantum correlations are challenging to observe, but they are very

interesting, since they correspond to rather significant fractional effects. For

example, H. J. Kimble’s group used phase-dependent Squeezed Light to

make a spectroscopic measurement with about 2-fold better Signal/Noise

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than the naive shotnoise limit [12]. To observe strong Squeezed Light

effects, it is essential to minimize optical losses, as they work to revert the

Statistics toward the thermal limit. Regrettably, noise from technical sources

will grow linearly in the laser power, while the advantage due to squeezing

will grow more slowly. It seems that getting a factor 10 amplitude S/N

improvement will be incredibly difficult.

Coherence of the Laser Field Enables Frequency-Diagnostics

The Bell Labs laser design success had grown out a semiclassical

view of how Optical Masers would operate. Yes, amplification would be

provided by quantum mechanical atomic systems, rather than radio tubes or

klystrons, and yes each atom could contribute just one photon to the field in

each event. But still, considering how huge is the number of photons in the

field, the discreteness probably will hardly matter. Almost immediately the

Bell-Labs team was testing this understanding by combining two separate

laser beams into a single coaxial beam, and shining this onto the sensitive

surface of a high-speed photodetector. They already were thinking of each

laser oscillation as being an essentially classical field, satisfying reflection

boundary conditions at the two mirrors. So this stable-and-repeating

bouncing specification would define the possible wavelength(s) of the

generated laser light. By luck and design the discharge was wonderfully

calm, so one could expect the gas’ refractive index would be essentially

constant. Thus the interferometric boundary conditions would essentially

define the oscillation frequency and, accordingly, one would expect to see

a sharp optical frequency come out of this device. With two lasers’ sharp

frequencies on the nonlinear detector’s surface, one should expect the

difference frequency to be generated, which it was. I can still remember

hearing the audio beat whistle that Javan had recorded when his two lasers

were tuned almost to the same optical frequency. It was a~1 kHz difference

between two sources at 260 THz!

Actually the linewidth of these beats was remarkably narrow. We

already expected that based on the numbers noted above: a stream of ~10'°

photons/s would have random power fluctuation of ~10° relative to the full

power. So the optical phase could be extremely well defined. However the

laser’s Schawlow-Townes linewidth calculation includes the role of optical

loss, which actually limits the laser coherence, giving ~ milliHz linewidth

expectation.

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In principle then we have a radiation of incredible sharpness, and

should be ready to seek interesting physical effects. The immediate

disappointing truth is that this tiny predicted laser phase fluctuation will be

completely masked by noise of technical origins. We already noted that the

strongest definition of the oscillation’s frequency is fixed by the

interferometric standing-wave condition bouncing on the laser cavity

mirrors. But the lab is a noisy place, seismically speaking, with a quiet lab

having a ground noise of ~3 x10° m/ JHz in the vibration frequency band

say | — 30 Hz. A laser cavity is some fraction of a meter in length, so it will

be difficult to make a system arbitrarily stiff. Rather, some important

fraction of the ground noise will appear as cavity length variations, and

therefore laser frequency variations. Suppose we say only 1% couples in to

relative length changes. One can instantly see the scale of the problem: ~10°

10 fractional frequency variations will be our a priori scale. Even

temperature variations will be painful, since the 10'° scale already

corresponds to a few millikelvin temperature change for low expansion

materials like fused silica. We can make progress by locking the laser to a

stable reference cavity [13]. Optimizing for vibrational integrity, we will

use a stiff structure for mounting the reference cavity mirrors, and then

mount the assembly with a horizontally soft suspension. By focusing on the

vibration isolation, Bergquist has obtained [14, 15] a record narrow laser

linewidth ~0.16 Hz! Another approach seeks to minimize the cavity

acceleration sensitivity. By use of a vertically-symmetric mounting [16] of

the reference cavities, our group recently reported Hz-level laser linewidths.

Coherence of the Laser Beats Enables Frequency- Based Laser Control

Considering the small intrinsic phase noise of the laser source, and

the rather high power ~ mW, heterodyne detection of the beat frequency

between two laser sources yields an interestingly high Signal/Noise ratio.

Even with very short averaging times, say 1 ts, we have generous S/N

performance. Additionally, for such short times a well-engineered laser will

scarcely respond to the “garbage effects” of real life in the lab (temperature

variations, power-supply variations, vibrations ...) — within 1 us these have

not changed the system very much. The duration of the perturbations is too

small for them to begin to wreak havoc with the stability of the frequency-

defining cavity. So we actually can make useful measurements of the laser’s

phase in such a quick time frame that the problems are not yet apparent!

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le?

One begins to see a strategy coming up: We will quickly measure what the

laser actually is doing, compared with our desired behavior, and then use

feedback onto suitable actuators to control the laser’s frequency. If we can

make the corrections quickly enough and accurately enough, then the

controlled laser will very closely approximate the ideal frequency-stable

laser we need.

Implementation of this servo-control feedback concept is a multi-nuanced

thing, in the perfection of which this author has invested something over 40

years of active work. It has led to a lot of interesting and useful electro-

optic tools and techniques.

The Relative High Power of Lasers Empowers Nonlinear Spectroscopy

and Sharp Resonances

Let’s begin with the first approach to observation of narrow atomic

resonances, using Saturated Absorption Spectroscopy. These phenomena

were studied first within a laser cavity by Bill Bennett using the dispersion

effects associated with the active Neon laser gas. Owing to the Doppler

Effect, the Neon atom’s natural resonance linewidth of ~10 MHz becomes

masked and broadened to ~ 1500 MHz. Thus most of the gas atoms are

detuned, and in a velocity-specific way. Some atoms have velocities near

the special one giving the Doppler shift that will bring them into resonance

with the intracavity laser field. Actually there are two such velocities to

consider, since the laser beam goes both directions as it is bouncing back

and forth between the mirrors. These resonant atoms will interact rather

strongly with the field, leading to an increased decay rate for excited state

atoms of that velocity — their inverted population gets converted into cavity

photons! If we imagine a plot of the population difference (upper state

minus lower state populations) we can expect to see a local and rather

narrow dip around the velocity which is being converted from population

inversion into light quanta. Actually there are the two mirror-symmetric

dips as noted before. The interesting effects come when we let the laser

frequency be tuned toward the atom’s rest-frame frequency. Then the

resonant atoms will have lower and lower Doppler velocities, until finally

the selected velocity is zero. Now a new thing happens: when detuned, we

had two groups of active atoms contributing their power to the laser output.

When we reach the central tuning, both running-wave fields interact with a

single atom velocity group. So with fewer atoms contributing, the laser

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power decreases conspicuously, but only at the central tuning. This feature

in the power output with laser tuning could be used for locking the laser to

this central tuning dip, which is called “Lamb’s dip” after Willis Lamb

whose early theoretical work made clear this origin of the experimentally-

observed effect. (His Nobel Prize in 1955 was for his work on the new sub-

hyperfine structure in the Hydrogen spectrum.) As it turns out, operating

pressures for optimum laser operation were rather large (~3 Torr, 400 Pa),

which led to substantial probability of atom-atom collisions, even during

the few 10’s of ns optical lifetimes. So the Lamb dips would be broader and

less deep, and had to be observed against a somewhat-peaked Doppler

profile representing the distribution of available atom velocities. In addition

to reducing the Lamb-dip contrast, significant frequency shifts were

generated [17]. One could not arbitrarily reduce the gas pressure since the

discharge pumping mechanism actually populated a metastable He* level,

and collisions were needed to transfer this excitation to the Neon atom

component in the discharge. So even though the wavelength of the laser’s

characteristic coherent light was more-readily-measurable than the

incoherent light from the krypton discharge lamp (the existing wavelength

standard), in fact the lasers’ pressure shifts were simply too large to accept.

Particularly this was the case since the discharge technology of the day led

to important change of the fill gas pressure and species ratio with operation,

due to electrode sputter-pumping.

The clearly important idea of separating the amplifier and the

reference gas cells’ functions was soon introduced by Lee and Skolnick.

More discussion of those interesting developments is available elsewhere

[18, 19], but for our present purposes we do need to consider some of the

essentials. Since the purpose was to have a sheltered life for our reference

atoms, it was attractive to be thinking in terms of absorption, rather than

amplification. Then we didn’t need any discharge or optical pumping of the

reference quantum resonators. Of course, to be able to use Lamb’s nonlinear

resonance for frequency stabilization, we certainly needed to be able to tune

the laser to the reference cell’s resonance frequency. Nowadays, this is no

big problem, by just using tunable lasers. At that time, the best idea to get a

wavelength coincidence would be to use molecules as the absorbers — then

we would have zillions of absorption lines to choose from. The modern

champion for this approach is molecular Iodine, with narrow useful

absorption lines from the Near IR down to ~500 nm. For other molecules,

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utilizing transitions only between vibrational-rotational states, typical

wavelengths are in the IR from ~2-10 micrometers range.

The first such dual-component optical frequency reference system,

and still one of the better ones, uses a HeNe discharge cell to provide gain

and laser oscillation at 3392 nm [18]. Also contained in the laser cavity is a

cell containing CH4 molecules, plain old tetrahedrally-symmetric methane,

which has interesting lines that can be reached with the HeNe laser. To be

brief, the necessary emitter/absorber spectral overlap 1s arranged by

selection, based on good luck! The IR absorption band utilized, v3, is a

strong fundamental vibration band, providing 0.18 cm absorption

coefficient per Torr. Of course having the absorber gas inside the cavity

means we don’t need very much absorption to have an impact on the laser

dynamics — just a few percent would be fine, since it would then be roughly

/2 the loss associated with the output-coupling mirror. At 10 milliTorr, the

associated pressure broadening of the CH4 resonance would then be ~160

kHz, similar to the 130 kHz broadening associated with the molecular free-

flight ate the ei sete ais ata beam, of 0.3 mm si diameter

lot LSS

PEP REe

Pa See

Figure 1. Saturated absorption peak in CH, molecules. HeNe laser at 3.39 um is excited

by rf discharge. CH, cell at 12 mTorr (16 mBar) is located inside laser cavity. Power output

is 300 ~uW and peak contrast is ~12%. Peak width is ~270 kHz HWHM. At maximum

power (~0.8 mW) contrast is ~15%. Cavity free spectral range is 250 MHz. Note cross-

over resonances in two-mode region near cusps. Hysteresis of scan causes trace doubling.

Importantly, the pressure-induced shift turns out to be very small for

these transitions, only ~1 kHz under these conditions.

So we are talking about a system with a resonance in the power

curve of ~0.6 MHz FWHM, with perhaps 5% relative contrast on the total

laser output of say 200 uW. A little calculation leads one to a

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Signal/ShotNoise ratio ~10° in a 1 Hz measuring BW, while we’re looking

at the sub-MHz —wide peak produced at the central tuning, when both cavity

running waves are bleaching the same absorbing molecules and thereby

reducing the intracavity absorption losses. If this S/N were optimally used,

the laser could be stabilized to have sub-Hz frequency deviations measured

in | s intervals. In 1968 when this Saturated Absorption Optical Frequency

Reference business began, our detectors and preamplifiers were not so

good, and we didn’t begin to approach the shot noise limit — that would have

been a frequency (in)stability of ~2 x10" at 1s. Early on, we did get dv/v

~1 x10, which was soon improved to 3 x10" with better detectors and

signal processing.

By locating the sample cell outside the laser resonator, the physical

situation could be more-readily analyzed, and this arrangement was

employed by Bordé, and by Hansch, and by Chebotayev’s group in early

experiments. The interesting details are discussed in textbooks: see e.g.

Letokhov & Chebotayev [20], Stenholm [21],and Levenson & Kano [22].

Now we consider the transit-time linewidth issue.

Free-flying Molecules see a Light Pulse: two views of the Uncertainty

Principle

For these transitions, the radiative lifetime (~ ms) was much larger

than the transit time of the essentially free-flying molecules in crossing the

laser beam. At low pressure the saturated absorption linewidth was not

collisionally nor Doppler limited, so it could be immediately observed that

the resonance linewidths could be reduced by increasing the field/molecule

interaction time. Larger beams helped. So did liquid Nitrogen cooling of the

glass cell. So a serious study began to really understand the lineshape in the

free-flight regime. Chebotayev and his colleagues developed the theory

analytically near the low-pressure, low optical power limit [23]. The JILA

theory was based on computer integrations of the Density Matrix for

absorbers making a free transit through the assumed Gaussian light beam

mode [24]. Low intensity and weak interactions were assumed to simplify

the calculations, but soon it became clear that most of the observed signal

would be contributed by a very small number of slow molecules. The

theoretical result is a logarithmic cusp at the exact line center. With long

interaction times, even a “weak” power would lead to saturation and other

strong-field effects.

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We need low velocity in the longitudinal direction so that the

molecule wouldn’t cross wavefronts axially, and thereby begin to develop

Doppler-related phase modulation. Effectively molecules should fly

perpendicular to the axis, and leave the wavefront after the transit with only

<1 radian geometrical phaseshift. We also need low transverse velocities,

since a longer transit time will be directly imaged into a narrower line. We

can see ovet ~ | will yield 5v = B vin/wo, dv is the HWHM of the observable

resonance, vin is the thermal velocity, wo is the Gaussian beam radius, and

6B is a measured parameter. Experimentally we found B vin = 88 kHz mm

for Methane at room temperature. Laser mode radius wo values from 56 um

to 9 cm were measured, with corresponding HWHM values from 1.6 MHz

down to 940 Hz. (The interesting substructure will be addressed

momentarily.) First it is useful to consider the transit-time broadening in the

Fourier-dual domain: angular divergence. Corresponding to a Gaussian

beam radius wo there is a minimum angular divergence of the collimated

laser beam of 60 = A/ 2mwo. The k-vector spread, particularly the non-axial

components lead to a velocity-dependent Doppler shift of the same sign for

both running waves, which will appear as broadening and shift of the

resonance. Of course with a smaller mode diameter, the angular content 1s

increased, and more broadening will appear spectrally.

While molecules typically do not have the “closed” optical

transitions analogous to those needed for normal laser atom cooling, polar

molecules do have a dipole moment. So with some electrical effort, one can

arrange Sisyphus-like molecule slowing by switching the sign of the strong

applied electric field, as shown by Meijjer’s group [25]. More recently Ye’s

group has achieved unprecedented high resolution microwave spectroscopy

on Stark-slowed OH free radicals [26]. Certainly this will be an interesting

frontier!

Other important directions are high sensitivity detection and

improving the accuracy of locking to the molecular signals. For example

some JILA work (“NICE-OHMS”) shows a road to sensitivity increase by

combining cavity enhancement and rf sideband techniques [27]. A

fascinating physics avenue is the search for a parity-related frequency shift

between suitable enantiomers [28]. Other important laser applications are

considered in Svanberg’s book. [29]

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Momentum transfer from Light to Molecules — the Recoil Splitting

A full treatment of radiative interactions must include the field and

molecular momenta, as well as the photon numbers and internal states of

the quantum system. Such a treatment is essential for the case of pumping

atoms with closed energy levels, which can allow the repeated interactions

and deep velocity cooling celebrated by the 1997 Atom Cooling Prize of

Phillips, Chu, and Cohen-Tannoudji. For the molecular sample of interest

here, there are many decay channels, and likely even impact on the vacuum

chamber walls before any particular molecule reappears in the laser fields:

so a single interaction picture is reasonable. A clear observation of the

transfer of momentum from field to atomic system is available with

Saturated Absorption Spectroscopy, basically because it is a two-step

process. Let’s consider absorbers that initially have essentially zero velocity

along the light beam. Then the left-running light beam can be tuned to

v= mt of = : , the extra (recoil) energy being needed beyond the

transition energy Vo to provide the kinetic energy associated with the recoil

momentum the molecule will have after the transition occurs. The opposite-

running beam will also deplete this zero-velocity group. So at this resonance

tuning, the resulting nonlinear decrease of molecular opacity will lead to a

peak in the transmission spectrum, and it 1s shifted slightly to the blue of

the rest frequency. Another interesting case occurs when the molecules have

a velocity v=h/ MA, i.e., there is enough molecular momentum initially

so that when the red-detuned laser interacts with this molecule, the photon

and molecular momenta just cancel, and the original kinetic energy can

make up for the photon’s energy deficit. The result is an excited molecule

with zero axial velocity. Now the laser beam in the other running direction

will experience amplification from this particular tuning condition, again

leading to a relative peak in the sample’s transmission. With the molecule

initially possessing some kinetic energy, the laser tuning for this upper-state

hv naed 3

= |. So considering photon

resonant condition will be Vv = v[1-

recoil, the nonlinear interaction is associated with either the ground or

excited state population being accessed by both beams for the same

detuning, namely zero velocity in either one of the two states. For methane

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the splitting between the two peaks is 2.163 kHz and may be seen clearly in

Figure 2 [30].

F= 7-6 F=8—-/7

Magnetic Hyperfine

structure - 3 peaks

Recoil doublet

splitting of hfs

20 kHz detuning

Figure 2. Recoil Splittings of Hyperfine-Structure Peaks in free-flight Methane Molecules.

The vertical strokes indicate the positions of the two recoil components in one of the

Hyperfine components.

While the JILA and University of Paris Nord work exploited mainly

the large diameter optical beams to gain a longer molecular interaction time,

Chebotayev, Bagayev, and colleagues 1n the Novosibirsk group made good

use also of another physical idea, namely the use of super-slow molecules

to contribute the main part of the observed signal. In this way an additional

20-fold linewidth reduction to <50 Hz was achieved [31]. An important

aspect of this approach is that the total 3-D effective molecular temperature

is below 0.1 K, leading to a much-reduced second-order Doppler shift, of

<< | Hz. An average velocity 13x below thermal for slow C2HD molecules

was shown by Ye et al. [27], and was feasible only because of the very large

sensitivity provided by the NICE-OHMS technique.

Other Optical Frequency References Based on NonLinear Spectroscopy

Many research groups have been attracted to working with laser

stabilization for Measurement Standards applications, such as

interferometric calibration of gage blocks that serve to check reference

standards used by industry. For this kind of application it is highly desirable

that the reference laser beam be visible, as well as stable enough and

reproducible enough. A huge success in this area is the 633 nm HeNe laser

with an intracavity Iodine cell, and well developed systems of this type are

even available commercially. This HeNe/I2 system was the one whose

frequency was measured by the NBS efforts in the early 1980’s, with an

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uncertainty of 70 kHz. (Being the first measurement of such a visible

system, it is perhaps understandable that several of the uncertainties were

far from fundamental in their origins.) Other labs joined in and over the next

decade many labs gained experience and a few had frequency

measurements confirming the NBS result. Slowly it became acceptable to

reconsider the definition of the International Unit of Length, the SI Metre.

As may be seen, the world of spectroscopy offers us an unending

garden of fascinating details. Presumably Parity-Non-Conservation will

lead to a next generation of fine structures in chiral molecules, particularly

with the development of cold-molecule techniques. But enough about the

“ticks” of the clock: now we must return to the main story, the development

of frequency stabilization and cycle-counting measurement tools — The

inside Gear-Works of the Optical Clock!

Measuring Optical Frequencies with Optical Combs

The Metre redefinition of 1983 was not really a kindness to

metrologists tasked with actually measuring some physical parts, because

the practical methods for application to measurements were not yet spelled

out. But it was a boon to the metrology researchers: it became their task to

explore just which good stabilized laser system would have the optimal

properties for precision interferometry, for outdoor surveying, for servo-

loop guidance of milling machines, for ... ? So within a dozen years after

the redefinition there were at least 10 well-developed optical frequency

standards, as illustrated in Fig. 3.

As may be seen in Fig. 3, there are stable frequency sources

available from roughly 10 um (30 THz) to ~280 nm (~1PHz), well beyond

the visible range. It was striking that the difference between lines were

surprisingly similar frequency intervals, ~88 THz, approximately the

frequency of the CH4 - stabilized laser. This led to schemes where doubled

frequency of one laser would be compared with the sum of the two

straddling lasers. Some “pocket change” of frequency, a few THz, could be

synthesized as sidebands using a Kourogi comb, based on a microwave

modulator 1n a cavity whose length provided resonance enhancement of all

the generated sidebands [32]. In such a way we measured the 532 nm Iodine

standard in terms of the difference of frequency between twice the HeNe

Iodine system at 633 nm, and the Rb two photon line at 782 nm.[33]

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—___—___» Frequency

0 88 192.6 266.2 281.6 385.3 456 473.6 563 617

Rb/2 15/2

CH eGrb a raGHDERb CxtleNe sh oel

a 5590 elo Om 26 IRSA pop verish C5

1064

Figure 3. Stable Lasers based on NonLinear Doppler-free Resonances in Gases (1995).

The frequency axis (above) is in THz units, the wavelength scale (below) is in nm.

This was our introduction to the elegance of having an optical comb

—a coherent ensemble of spectral lines whose frequencies are accurately

represented by a simple formula. Our system covered just a few nm

wavelength. How sweet it would be to cover the entire visible band, giving

several million accurately known frequency reference lines all at once!

One way to broaden this Kourogi comb’s spectral width would be

to provide intracavity gain, to compensate the modulator’s optical losses, a

scheme which was demonstrated by Diddams using an OPO crystal also

inside the resonator. Oscillation and generation of hundreds of FM

sidebands were easily observed [34]. For some tuning conditions the phase

of the several spectral components led to pulse generation, rather than pure

FM emission. In many ways this was just the hard way to do what the Ultra-

Fast Laser scientists appreciated about the Ti:Sapphire self-mode-locked

lasers: stable, self-organized, ultra-short high repetition rate pulse trains.

Elsewhere our group’s papers discuss the technical richness of these lasers

and the comb business [35]. This is just one further note about the mutual

coupling between “independent” research streams: we switched to

Ti:Sapphire fs lasers and never looked back.

Coincidentally, in these final days of the last Millennium, this laser

community received a fundamentally-important gift from the laser industry.

There would probably be no widely-used frequency combs without it. This

“sift” was the introduction of high-power visible lasers, based on

frequency-doubling the output of a laser-diode-pumped Nd solid state laser.

These were immediately put to use replacing the fussy and quite noisy

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Argon Ion laser in wide use for pumping the Solid State lasers. Competitive

forces led these new pump lasers to be well engineered, with intensity

stabilization to yield exceedingly low levels of residual amplitude noise.

This property is crucial because of the way a self-mode-locked laser

operates — these Ti:Sapphire lasers are self-mode-locked by a self-induced

optical lens which makes the cavity less lossy when the laser modes are all

synchronized to form an “optical bullet” in the laser medium [36]. This

temporary lens is formed by the radial index gradient, induced and present

only if a light bullet is present. So the laser cavity 1s originally set up to need

this extra focusing to produce low-loss cavity modes, and after the laser is

started in the pulse regime, stable self-mode-locking is maintained.

Consider that the pulse lengths are only ~10 fs, while the repetition periods

are ~10 ns. With ideal synchronization, the peak power/average power ratio

is ~10°. A typical laser will emit ~0.5 W through an output mirror of 5%

transmission. So we have 10 W average internal power, and 10 MW peak

power, which is focused to a ~14 um radius spot in the Ti:Sapphire laser

crystal. This active area is only 3 x10 cm’, so with 10 MW peak power we

have 3 TW/cm’! The associated electric field is ~10% of the interatomic

fields in the crystal, so it is not so surprising that a significant optically-

induced increase of the index of refraction occurs (optical Kerr effect). The

low amplitude noise of the pump laser is now seen to be critical: an

intensity-dependent phase-shift though the laser crystal will produce

amplitude > frequency conversion and thus unacceptable phase noise if the

pump is noisy. In a good case the linewidth of laser comb-lines without

frequency control is ~3 — 10 kHz due to this cause, before the servo is used.

Details of the process have been studied [37].

So the pulse train leaving the laser 1s of ~500 kW peak power, much

of which we will focus into the special nonlinear fibers that brought in the

age of the Optical Comb. Because of the microstructure design of the fiber,

full light guiding is possible even with fiber core sizes of 1.5 -2 um

diameter. So now when we estimate the fiber’s active area, it is roughly

200-fold smaller than the laser’s, while the power level is ~20-fold lower.

The 10-fold higher intensity produces a 3-fold higher electric field in the

silica fiber, being now essentially comparable with interatomic field and

setting the stage for SERIOUS NonLinear interactions. Forget Mr. Taylor’s

expansion here: this is strong signal NonLinear physics! All frequency

components from the laser are mixed with each other, resulting in a drastic

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spectral broadening. By the fiber’s optical design, a broad range of optical

frequencies can travel through the fiber with little speed variation, which

allows these frequency conversion processes to remain phase-matched and

accumulate power into the newly created frequencies. Essentially, in a few

cm of length, the input spectrum is converted to white light and covers an

octave or more of optical bandwidth. Actually the light is not quite “white”

since it still carries the basic heartbeat of the original fs laser, for example

100 MHz. As explained previously, this intrinsically generates a comb

spectrum with component widths just connected to the spectral resolving

power employed. Eventually, at the kHz level and below, the broadly-active

phase modulation processes that affect all lasers will broaden these lines

also (before the servo control is ON).

Complementarity, Cooperation, and Competition

The Basics

The remarkable insights of Professor Hansch’s Stanford work [38]

were published in ~1978, and already demonstrated using a repetitively-

pulsing laser to generate an optical comb which could serve as a spectral

ruler. However the bandwidth of the covered spectrum was too small for

general frequency measurements — only a GHz or two. Since these intervals

could be spanned in other ways, the methods were not widely adopted.

Basically there was not a technical growth path available at the time.

Principle, yes; Tool, no.

The hard work, straight-ahead “government” approach to frequency

measurement had been demonstrated at NBS in 1972 [39], following the

pioneering work of Ali Javan’s MIT frequency measurement group (See

references in [40]). But this was a heroic effort and mainly only national

standards laboratories took much interest. Laser after different laser had to

be lined up and frequency-related to the doubled frequency of its

predecessor, to step-by-step build up the frequency measurement chain.

This kind of work required development of frequency- and phase-locking

schemes now in wide use. We also got a “one-of-a-kind” physical result, a

single laser frequency was measured by the cooperative and extended work

of the NBS group [41]. But it was enough to get the Metre redefinition

process started.

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The Divide and Conquer Scheme

In a notable paper (1990), Professor Hansch and his colleagues

suggested an excellent way to simplify the frequency chains: one should use

the difference frequencies between lasers as the entities that were

harmonically marching up the spectrum [42]. In this way, the ensemble of

lasers would all have nearly the same wavelength, and could be built

essentially by duplication of a basic diode laser unit. Then with nonlinear

crystals, fast photodetectors, and suitable phase-locking electronics one

could progress from microwaves to optical frequencies. This system also

felt rather elaborate and specialized, but was used with good results in

Garching. A related strategy was developed at NRC [43], based on

difference frequencies, using COd2 lasers. Inspecting such a system, one

came to see that the first 9 or 10 of the 14 stages served only to get the

frequency up into the low THz range.

Then in 1994 came Kourogi and Ohtsu’s multiply-resonant cavity

approach, allowing one to reach a few THz in a single step [32]. Eventually

the buildup of phase noise — according to the high harmonic of the original

microwave source — would have been a problem in going into the visible

range. But the fs laser Comb arrived and offers an easier and better way.

See below.

A Brief History of the Optical Miracle of 1999 - 2000

Fibers for Spectral Broadening

By now the JILA group had accepted the fs laser as a great source

of pulsed laser light. Ours had ~ 80 nm bandwidth at 800 nm. But the optical

frequency standards we wanted to connect were at 1064 nm (fundamental

of Iodine-stabilized Nd laser) and 778 nm (Rb two-photon-stabilized diode

laser). An ordinary communication fiber was found to be just barely capable

of spectral broadening the necessary amount — 104 THz. This paper was

submitted at the end of September 1999 [44].

MicroStructure Fibers for Serious Nonlinearity

The Conference on Laser and Electro-Optics of June 1999 had a

spectacular post deadline presentation by a Bell Labs team [45], wherein a

normal fs laser pulse evolved its color in a dramatic way in propagating

through a few meters of a special fiber. Such a fiber did make collimated

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white light, in the form of stably-repeating pulses, just as Ted Hansch had

postulated for his (unpublished) frequency measurement proposal. Using

that previously-unknown light source, most of the rest should be possible.

(Seeing the repetitively-pulsed laser-like white light the fiber generated

instantly convinced me that Ted’s Concept actually could be a real and

physical possibility! Without a repetitive white-light laser, there was no

chance.) Lengthy appeals for scientific collaboration with the fiber owners’

organization ultimately became irrelevant due to the miraculous appearance

in JILA of a sample of this Magic Fiber. The concept of “band-gap” or

“Photonic-Crystal” fibers was introduced in 1996 by Knight et al., pointing

out the possibility of controlling the spatial modes and effective group

velocity dispersion by the mechanical design of the air holes [46]. Our first

JILA experiments were made using microstructured fiber drawn from a

preform prepared on September 10, 1997 by Robert S. Windeler of Bell

Labs [47], using a construction technique of his own devising. A broad

range of fiber designs was investigated in Bath, UK, by P St. J Russell and

colleagues.

The Race is ON

Of course in JILA we didn’t know that the Garching team had

already gone from a plan to the first demonstration of a comb-based phase

coherent link from microwaves to the visible, and had submitted their Phys.

Rey. Letter in November 1999. Even before we got the Magic Fiber! They

used a comb of somewhat limited bandwidth, 44 THz, but their divider

stages could connect the optical frequency with the 28" harmonic of the

difference between the comb’s edges. It is a beautiful result, and appeared

finally on 10 April 2000 [48]. In the meantime the JILA team was working

hard with the Magic Fiber’s white light output to implement and

demonstrate our phase-coherent locking of the carrier-envelope offset

frequency in terms of the laser’s repetition rate. Our Disclosure of the

scheme called this “Self-Referencing”. The control electronics we built had

a digital click switch so the phase could be set on any integer multiple of

1/16 of a phase-slip cycle per pulse. The JILA experimental demonstration

was based on interferometrically determining the carrier-envelope phase

difference between two optical pulses, separated by one intervening pulse.

Finally the new electronics worked, the experimental data were clear and

our report [49] appeared in Science on 28 April 2000. A PRL joint article

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celebrating the success of the combined Garching, Bell Labs, and JILA

teams appeared on 29 May 2000 [50]. Within the next year there was an

avalanche of absolute optical frequency measurements from labs all over

the world. This was a glorious chapter in optical physics history, in no small

part because of the high mutual respect of the two teams for each other,

aided by the complete openness fostered by the frequent exchange of

postdocs Scott Diddams and Thomas Udem between the two hotly-

competing groups.

Some Frequency Measurement Results

Many laser frequency standards were being actively studied worldwide so

that, when the Comb breakthrough came, there were many things to be

accurately measured — many for the first time. A few of the world-wide

results include the work shown in the following Table.

Table I. Measured Optical Frequencies. The reference atom/molecule and its transition

wavelength are indicated, followed by lead author and institution, the journal name and

date. The first fs Comb measurement was Hydrogen, by Reichert ef a/. The first direct fs

optical measurements were by the JILA team (Jones). Note the brevity of time between

publications!

The comb technology spread explosively in 2000, bringing vast

simplification of optical frequency measurements, along with a steady

improvement in the accuracy. Very soon after the initial measurements, it

has become the case that the comb’s measurement precision can exceed that

of the standards being measured. Recent tests at NIST, BIPM, and ECNU

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[51] confirm the earlier MPQ experiments [52] showing that the comb

principle is strictly correct up to a measurement precision of more than 18

digits.

Molecular Iodine Optical Frequency Standard

The Iodine-stabilized Nd:YAG laser is a sweet spot in the stabilized

laser domain, counting on its excellent performance and relative simplicity.

One system was made in Japan that met airlines cabin baggage limitations

and still delivered excellent performance [53]. Because of the Iodine’s great

atomic mass, the second-order Doppler correction for this system is only ~5

xl0'° and it is likely that independent reproducibility perhaps 5-fold

superior to this can come with improved technical realizations. In particular,

providing an offset-free modulation strategy is still a challenge. The

advantage of this system is its compactness and potentially reasonable cost.

Taken with an optical comb, one can have an attractive clock [54]. See Fig.

4. The frequency (in-)stability of all the 1 million optical comb lines is ~ 4

x10°!4 /Vr.

Recently stable Yb: YAG single frequency lasers became available,

with output tunable to 1029 nm. When frequency doubled, excellent

stabilization performance should be possible with the I2 transitions at 514.5

nm, considering that the linewidth 1s at least 5-fold smaller than for the 532

nm line [55]. Single frequency fiber systems can also offer this wavelength.

So What Comes Next?

In addition to the simplification of optical frequency measurements,

the resulting new capabilities are unbelievably rich in terms of the tools and

capabilities that have been created, and these in turn are reinforcing progress

in these contributing fields. This paper can’t even attempt to present a

myriad of delicious physical effects, which are normally understood as

being in different fields, but which in their now-unified relationships can be

seen as creating a truly remarkable and enabling advance of the research

tools available in optical science. But let me still give a few examples.

Winter 2016

132

{99 {$$ $—_——\\_\—

Improved fs comb

Before May, 2000 After April, 2001 standard deviation 16 Hz

over a month (6 x 10“)

inane

oe Bp danfebf th a ti hated atta

(CIPM Frequency 281 630 111.74 MHz)

Measurement over a year:

Mean Value: 17.240 kHz, Standard Deviation: 118 Hz (4x10

[@)

13 ) GigaOptics Laser

+ Danish fiber

(7 months later:

f4o64 - CIPM Frequency (kHz)

Jan. 23, 2002)

15 a me a ie a nT ae SF

Wl 2 We 432 440 444 506508510 726

Days

Fig 4. Long-term frequency stability of lodine-based Optical Clock. This figure conveys

the refinement and small frequency offset of this stable optical clock’s frequency from

previous, much less accurate measurements. With improved technology in 2002 the

uncertainty was further reduced to ~6 x10°'*.

After the frenzy of Generation I frequency measurements of Table

I, some of the Generation II comb applications in Jun Ye’s group include:

low-jitter time synchronization (~fs) between ultrafast laser sources [56];

coherent stitching-together the spectrum of separate fs laser sources so as to

spectrally broaden and temporally shorten the composite pulse [57];

precision measurement of optical nonlinearities using the phase

measurement sensitivity of rf techniques [58] ; coherently storing a few

hundred sequential pulses and then extracting their combined energy to

generate correspondingly more intense pulses at a lower repetition rate [59];

and searching for a change in the physical constants by the Garching team

[60]. Exciting topics of research for Generation III applications now include

connecting optical frequency interim standards at the sub-Hz level (in spite

of their different locations spectrally and physically), allowing precise

remote synchronization of accelerator cavity fields, providing stable

reference oscillators for Large Array Microwave Telescopes, and

potentially reducing the relative phase-noise of the oscillator references

used for deep space telescope arrays (NASA, VLBI ...) That’s part of the

first five years.

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133

And the next projects? What about 14.4 keV comb-line harmonics

to look at Méssbauer °’Fe nuclear resonances? Another sharp line is in '*!Ta

at 6.2 keV. How about parallel processing to determine biological activity

of a candidate drug, by means of CARS using synchronized pulse lasers to

excite specific ligand Raman resonances of a single molecule that was

attracted to and stuck by a particular test protein patch on a surface?

In a larger framework, we now find ourselves at an almost unique

point in the development of Science, where we the have remarkable ability

to “understand” practically all phenomena, to compute accurate predictions

from our equations, and to integrate a variety of details into our models.

Consider for example the GPS system, in which different kinds of physics

such as gravity and relativity are successfully merged with our sophisticated

atomic clocks — not to forget satellite dynamics and radio engineering and

computer software — so that in the total we have a coherent and highly useful

practical tool. Remarkably, the system is simple for the end user to apply.

We must count this GPS achievement as one of the all-time ultimate

technical success levels ever achieved.

The work recognized by the 2005 Nobel Physics Prize represents

entry of another dramatic, major and enabling advance, and one which we

can expect to show some flavors of the same breadth and character just

noted regarding GPS. But in these first moments after its birth, our opto-

electronic technology is new and 1s barely illustrated, not much beyond the

first cases of interest to frequency-standards people and metrologists. We

know that the accuracy of optical frequency measurements 1s now limited

to “just” 15 digits by the present microwave standard of frequency, but the

““Comb” technology actually allows two optical frequencies to be compared

with several orders of magnitude more precision. If the history of physics is

any guide, we realistically can expect to find some nice surprises ahead as

these capabilities become even more widespread, and are applied to

ingenious fundamental measurements by a growing and imaginative

community of “fundamental physics” scientists. After considering all the

known progress in Science, would you bet that we have already opened the

Russian Matryoshka doll of Nature and already found the ultimate inside

limit?

Winter 2016

Acknowledgements

The joy of interacting with superb young scientists is clearly one of

life’s treasures. Among these many I must single out for special thanks Jim

Bergquist, Leo Hollberg, Miao Zhu, and Jun Ye for their enthusiasm and

unique contributions to the JILA program. The NIST management 1s

enthusiastically thanked for accepting and sponsoring over the years a series

of risky proposals in Laser Spectroscopy. Particularly Leo Hollberg, Steve

Cundiff and I were glad they accepted the fs comb frequency synthesizer

proposal in Spring 1999. Scott Diddams and David Jones were the excellent

colleagues additionally involved in these experiments, and JILA’s research

force was hugely expanded when Jun Ye rejoined JILA in 1999 to start his

own group. As always, whenever Professor Long Sheng Ma was visiting us

from Shanghai our pace was strongly advanced. Visiting Scientists such as

Christian Bordé continue to be collaborators even three decades after their

JILA time. I am pleased and grateful to acknowledge that the work has been

supported in part by the NSF, ONR, AFOSR, and NASA, and for over 4

decades by the NIST. I benefited greatly from the knowledge and generous

sharing of ideas and opportunities by my NBS mentor, Peter L. Bender.

Above all I am indebted to my patient and insightful lifetime friend Lindy

Hall for her understanding, her great efforts and contributions to this

scientific work and, more importantly, to our joyous and fun life together.

It has been wonderful in the course of these 45 years to see a progression of

experiments and technical advances make possible this ultimate payoff in

the optical comb. Now we’re discussing if it’s almost time to clean my

office at JILA and pack up into a new camper unit to go out and further

explore another domain in the world.

Appendix: The Full Comb Story in an Undergraduate’s World

I’m glad you asked how to think about frequency combs. Suppose

you have a sinewave voltage or field. Then a plot in time shows a smooth

oscillation and a plot in frequency shows a single Fourier component,

namely a sharp line. Now add a few harmonics onto this wave. The

spectrum now has a few more lines at exact harmonic frequencies, while the

time picture has a rather complicated shape. By adjusting the phases of the

harmonics, we can begin to synthesize some disturbance in time that begins

to remind one of a pulse, or more exactly, a series of identical pulses. Carry

this a step forward by having a large number of harmonics. The more we

Washington Academy of Sciences

135

add, the sharper is the pulse we can synthesize, and of course the richer is

the spectrum of this wave. Going further in this direction of adding coherent

harmonics, the spectrum now has zillions of spectral lines, all at the

harmonics of our original sinewave. Carrying this concept to the visible will

require a few million (10°) harmonics for a source with 100 MHz basic

repetition rate. With the proper phase adjustments, the time domain pulse

can be 10° times sharper in time than the original sinewave. So we can

expect really narrow temporal pulses, and really wide spectral bandwidths.

This situation fits well with what we would expect from Fourier

analysis of a single pulse: such an impulse will have Fourier components at

all frequencies, with their nearly-constant amplitudes gradually decreasing

for frequencies above the reciprocal temporal pulsewidth. If we have a

repetitive pulse train in time, but insist to ask about its spectrum, we will

need an analyzer with a narrower passband compared with the repetition

frequency, otherwise it couldn't resolve the harmonic structure. But a

narrow spectral passband corresponds to a long temporal response time. So

the output of the spectrometer at any particular wavelength or frequency

setting will be the result of coherent addition of the contributions of many

pulses. While an individual pulse has a broad and continuous spectrum,

when we coherently add their spectral amplitudes we can expect to have

interferences that will modulate the spectrum. Adding more pulses

temporally (narrower spectral resolution) will give deeper modulation.

Eventually we arrive at very sharp spectral lines, evenly arranged as Fourier

harmonics. Until we encounter technical issues such as phase-noise of the

repetition rate, the sharper an analysis resolution we apply to the waveform,

the sharper will be the spectral lines we observe. So the spectrum does

indeed remind one of a "comb." You can demonstrate these ideas safely at

home for yourself easily in the electronics domain, but of course the optical

and electronics worlds should work the same ...

In fact, with the fs lasers used to generate these pulses, there is one

more little item of interest. That is that the laser can oscillate in any one of

its cavity modes, defined by having a repeating phase after going one loop

around the cavity. All the many modes involved have their own longitudinal

quantum numbers, essentially how many full optical cycles are contained in

the closed loop. This calculation clearly involves the wavelength-dependent

phase velocity, and some average of the propagation through the many

Winter 2016

136

optical components. Another reality is that the laser operates in a self-

organized repetitive pulsing mode. Effectively the laser's optical losses can

be made large enough to inhibit laser action, unless all the cavity modes can

adjust their phases to synthesize a delta-function spatially. The critical thing

is to have a short pulse when passing through the Ti:Sapphire crystal, since

the short pulse will correspond to very high peak power, and that will

interact with the laser rod's material in a quadratic way (optical Kerr effect)

to produce a positive lens: a bigger index on the axis where the intensity is

maximum. So the self-organized pulse situation is stable in which the laser's

cavity has a high diffraction-loss (doesn't have quite enough positive lens

power), but the losses are periodically remedied by a bullet of light which

uses its self-action on the crystal to produce the needed extra refraction that

makes the cavity losses be suitably less.

Now the pulse envelope that describes this light "bullet" results from

superposition of many cavity modes, and the shape will evolve if there are

temporal delay differences with wavelength. We are now just discussing the

group velocity concept, whereby the shape of a disturbance will evolve

unless all the frequencies have the same propagation speed. In the physical

laser we must include some optical elements specifically to deal with the

fact that blue light in the laser crystal will travel more slowly than red light.

To get the shortest pulses the time delays around the loop need to be

essentially the same, although you can see this becomes a little complicated

in that the laser pulses themselves act to influence the time delays. In any

case, the light which comes out of the laser's coupling mirror will be a

regular time series of sharp pulses, and will display a comb-like structure

under frequency analysis. However the underlying fast optical oscillations

will in general have a different phase each time the pulse hits the mirror's

surface. The fast oscillation's phase will shift a bit forward or backward

from one pulse to the next, and so the optical frequency comb may be offset

a bit from the strictly Fourier harmonic case we first imagined. The usual

case 1s a constant phase shift for each pulse, and so a constant rate of

accumulating a phase beyond the repetition-rate's harmonic. We have

developed an electro-optic scheme called "self-referencing" in which this

additional frequency, the Carrier-Envelope Offset Frequency, is stably

locked to the repetition frequency in a digital ratio. For example one could

choose zero for the setpoint ratio and thereby have a strictly harmonic comb.

With the offset = 1/2, one generates a comb offset by 1/2 the basic repetition

Washington Academy of Sciences

rate, which itself is of course the frequency comb's tooth spacing. See Refs

[48-52].

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Washington Academy of Sciences

14]

Nobel Lecture: Superposition, Entanglement, and

Raising Schrédinger’s Cat'

David J. Wineland

National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado

VI.

VU.

VIL.

IX.

80305, USA

Contents

al CALCIO 8 Nene eee ea re tee ed Nr OT REIT 14]

nome Bary Steps. Toward Quantum: @ontrol c.rc..,<.¢-osecercenetessseees 144

Controlling the Quantum Levels of Individual Trapped Ions ....147

Manipulating Ion Motion at the Quantum Level .....................0 152

SOL SSIs) ae OFS Oe ee en ee ae we eens Cee 156

char > COU TALAC LINN, SITTIN OD) 88 ceases het teva lee nts poate meee ee Io

b; Spectroscopy and quantum mictrology ..!....0.iaeaen st 163

PRAY 1 MO Saal ee eee 165

PRION EA OMCI Se. scars.ciccnioduersnar ne eceee ee cere eee ceametee es 165

BE SHERE BICC Sie sities cvs etc teuseicta nest ues gastaetch as oabendet ememtenen adel Sereeee ny cee 166

I. Introduction

EXPERIMENTAL CONTROL OF QUANTUM SYSTEMS has been pursued widely

since the invention of quantum mechanics. In the first part of the 20th

century, atomic physics helped provide a test bed for quantum mechanics

through studies of atoms’ internal energy differences and their interaction

with radiation. The advent of spectrally pure, tunable radiation sources

such as microwave oscillators and lasers dramatically improved these

studies by enabling the coherent control of atoms’ internal states to

deterministically prepare superposition states, as, for example, in the

! The 2012 Nobel Prize for Physics was shared by Serge Haroche and David J. Wineland.

These papers are the text of the address given in conjunction with the award. Reprinted

from RevModPhys.85.1103.

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Ramsey method (Ramsey, 1990). More recently this control has been

extended to the external (motional) states of atoms. Laser cooling and other

refrigeration techniques have provided the initial states for a number of

interesting studies, such as Bose-Einstein condensation. Similarly, control

of the quantum states of artificial atoms in the context of condensed-matter

systems is achieved in many laboratories throughout the world. To give

proper recognition to all of these works would be a daunting task; therefore,

I will restrict these notes to experiments on quantum control of internal

and external states of trapped atomic ions.

The precise manipulation of any system requires low-noise controls

and isolation of the system from its environment. Of course the controls

can be regarded as part of the environment, so we mean that the system

must be isolated from the uncontrolled or noisy parts of the environment.

A simple example of quantum control comes from nuclear magnetic

resonance, where the spins of a macroscopic ensemble of protons in the

state |) (spin antiparallel to an applied magnetic field) can be

deterministically placed in a superposition state

a|t)+ B|T)(la

specified duration. Although the ensemble 1s macroscopic, in this example

each spin is independent of the others and behaves as an individual

quantum system.

But already in 1935, Erwin Schrédinger (Schrédinger, 1935)

realized that, in principle, quantum mechanics should apply to a

macroscopic system in a more complex way, which could then lead to

bizarre consequences. In his specific example, the system is composed

of a single radioactive particle and a cat placed together with a

mechanism such that if the particle decays, poison is released, which kills

the cat. Quantum mechanically we represent the quantum states of the

+B =i by application of a resonant rf field for a

radioactive particle as undecayed = or decayed =|) and live and

dead states of the cat as |Z) and |D). If the system is initialized in the

state represented by the wave function I?) L) , then after a duration equal

to the half-life of the particle, quantum mechanics says the system

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evolves to a superposition state where the cat is alive and dead

simultaneously, expressed by the superposition wave function

v= |1)Iz)+|1)12)} (1)

Schrédinger dubbed this an entangled state because the state of the particle

is correlated with the state of the cat. That is, upon measurement, if the

particle is observed to be undecayed, one can say with certainty that the

cat is alive, and vice versa. But before measurement, the particle and cat

exist in both states. This extrapolation of quantum mechanics from

individual quantum systems to the macroscopic world bothered

Schrédinger (and a lot of other people). As one way out of the dilemma,

in 1952, Schrédinger (Schrédinger, 1952b) wrote

“... We never experiment with just one electron or atom or

(small) molecule. In thought experiments, we sometimes

assume that we do; this invariably entails ridiculous

CONSEeqUeNCces...”

But of course these days, this argument doesn’t hold and we can

in fact experiment with individual or small numbers of quantum systems,

deterministically preparing superpositions and entangled superpositions.

Our control is best when we deal with very small numbers of particles,

which enables us to realize many of the gedanken experiments that

provided the basis for discussions between Schrédinger and the other

founders of quantum mechanics. And, we can also make small analogs

of Schrédinger’s cat, which are by no means macroscopic but have the

same basic attributes. So far, it appears that our inability to make

macroscopic “cats” 1s due just to technical, not fundamental, limitations.

Admittedly, these technical limitations are formidable, but one can be

optimistic about increasing the size of these states as technology

continues to improve.

This contribution is based on the lecture I gave at the Nobel

ceremonies in 2012. It is mostly a story about our group at the National

Institute of Standards and Technology (NIST) in Boulder, Colorado,

whose combined efforts were responsible for some of the contributions to

the field of trapped-ion quantum control. It will be a somewhat personal

tour, giving my perspective of the development of the field, while trying to

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acknowledge some of the important contributions of others. For me, the

story started when I was a graduate student.

II. Some Early Steps toward Quantum Control

From 1965 to 1970, I was a graduate student in Norman Ramsey’s

group at Harvard. Norman, with his close colleague Dan Kleppner and

student Mark Goldenberg, had recently invented and demonstrated the first

hydrogen masers (Goldenberg, Kleppner, and Ramsey, 1960; Kleppner,

Goldenberg, and Ramsey, 1962). As part of this program, Norman wanted

to make precise measurements of the hyperfine frequencies of all three

isotopes of hydrogen, so I chose to work on deuterium. The experiment was

relatively straight- forward, complicated a bit by the relatively long

wavelength (~ 92 cm) of deutertum’s hyperfine transition relative to that

of hydrogen (~21 cm) (Wineland and Ramsey, 1972). Most importantly,

this experiment taught me to pay close attention to, and control as best as

possible, all environmental effects that would shift the measured transition

frequency from that found for an isolated atom. In addition to enjoying

the detective work involved 1n this, I also became hooked on the aesthetics

of long coherence times of superposition states (~1s in the masers), and

their importance in atomic clocks. Norman received the 1989 Nobel Prize

in physics for his invention of the separated-fields method in spectroscopy

and development of the hydrogen maser (Ramsey, 1990).

During my time as a graduate student, I also read about and was

intrigued by the experiments of Hans Dehmelt and his colleagues Norval

Fortson, Fouad Major, and Hans Schuessler at the University of

Washington. The trapping of ions at high vacuum presented some nice

advantages for precision spectroscopy, including the elimination of the first-

order Doppler shifts and relatively small collision shifts. The Washington

group made high-resolution measurements of the *He* hyperfine

transition, which has internal structure analogous to hydrogen, by storing the

ions in an rf (Paul) trap. One challenge was that detection by optical

pumping was (and still is) not feasible because of the short wavelengths

required. Therefore, in a heroic set of experiments, state preparation

was accomplished through charge exchange with a polarized Cs beam that

passed through the ions. Detection was accomplished through a charge-

transfer process & He* +Cs > *He + Cs") that depended on the internal

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state of *He* , followed by detection of the depleted *He* ion number by

observing the ions’ induced currents in the trap electrodes (Fortson, Major,

and Dehmelt, 1966; Schuessler, Fortson, and Dehmelt, 1969).

Although these experiments were what first attracted me to ion

trapping, my postdoctoral research with Dehmelt, starting in the fall of

1970, was focused on experiments where collections of electrons were

confined in a Penning trap for a precise measurement of the electron’s

magnetic moment or g factor. These experiments were started by Dehmelt’s

graduate student, Fred Walls, who later became a colleague at the National

Bureau of Standards. After a while, it became clear that systematic effects

would be much better controlled if the experiment could be performed on

single electrons. Therefore, the first task was to isolate a single trapped

electron. This was accomplished by first loading a small number of

electrons into the trap and driving their nearly harmonic motion (~ 60

MHz) along the magnetic field direction. This motion could be detected

by observing the currents induced in the electrodes (proportional to the

number of electrons). By adjusting the strength of the drive to a critical

level, occasionally one of the electrons would gain enough energy to strike

a trap electrode and be lost. Steps in the induced current level could then

be used to determine when one electron was confined in the trap

(Wineland, Ekstrom, and Dehmelt, 1973). Subsequent experiments on

single electrons by Robert Van Dyck, Paul Schwinberg, and Dehmelt were

used to make precision measurements of the electron’s g factor (Van

Dyck, Schwinberg, and Dehmelt, 1977; Dehmelt, 1990). For this and the

development of the ion-trapping technique, Dehmelt and Wolfgang Paul

shared the Nobel Prize in 1989, along with Ramsey.

The modes of motion for a single charged particle in a Penning

trap include one circular mode about the trap axis called the magnetron

mode. For the electron g-factor experiments, it was desirable to locate the

electron as close to the trap axis as possible by reducing the amplitude of this

mode. This could be accomplished with a form of “sideband cooling”

(Wineland and Dehmelt, 1975a, 1976) as demonstrated by Van Dyck,

Schwinberg, and Dehmelt (1978). Around this time, I was also stimulated

by the papers of Arthur Ashkin (Ashkin, 1970a, 1970b) on the possibilities

of radiation pressure from lasers affecting the motion of atoms. In analogy

with the electron sideband cooling, Dehmelt and I came up with a scheme

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for cooling trapped-ion motion with laser beams (Wineland and Dehmelt,

1975b) (see below). The cooling could also be explained in terms of

velocity-dependent radiation pressure as in a concurrent proposal by Ted

Hansch and Art Schawlow (Hansch and Schawlow, 1975). We didn’t

anticipate all of the uses of laser cooling at the time, but it was clear that it

would be important for high-resolution spectroscopy of trapped ions. For

example, the largest systematic uncertainty in the ~He* experiment

(Schuessler, Fortson, and Dehmelt, 1969) was the uncertainty in the time

dilation shift, which would be reduced with cooling.

In the summer of 1975, I took a position in the Time and Frequency

Division of NIST (then NBS, the National Bureau of Standards). My first

task was to help make a measurement of the cesium hyperfine frequency,

the frequency reference that defines the second. The apparatus, NBS-6, had

been built by David Glaze of the Division. It was a traditional atomic beam

apparatus but had a relatively long distance between Ramsey zones of

3.75 m. With it, we realized a fractional accuracy of 0.9 x 10°? (Wineland

et al., 1976). At that time, the Division was more service oriented, with very

little basic research. Fortunately my group leader, Helmut Hellwig, had a

progressive view of the Division’s future and was able to obtain NBS

support to initiate laser-cooling experiments. That support, along with

some seed money from the Office of Naval Research (ONR), enabled us

to start a project on laser cooling in the fall of 1977. With Robert

Drullinger (a local laser expert) and Fred Walls, we chose to use ~“Mg*

because of its simple electronic structure and Penning traps, because of our

prior experience with them. This was a very exciting time, being able to

work on a project of our choosing, and by the spring of 1978, we had

obtained our first cooling results (Wineland, Drullinger, and Walls, 1978).

In our experiments we observed currents in the trap electrodes induced by

the ions’ thermal motion and hence had a direct measurement of the ions’

temperature. Meanwhile, Peter Toschek’s group in Heidelberg (joined by

Dehmelt, who was on sabbatical) was working toward the same goal,

using Ba” ions confined in an rf-Paul trap. They, with colleagues Werner

Neuhauser and Martin Hohenstatt, also observed the cooling at about the

same time (Neuhauser ef al., 1978), through the increased trapping lifetime

of ions. In a near coincidence, although there was no contact between the

groups, the manuscripts were received by Physical Review Letters within

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one day of each other (Peter Toschek’s group “won” by one day!). The

cooling observed in both experiments is typically called Doppler cooling,

where the oscillation frequency of the ions’ motion is less than the

linewidth of the cooling transition. Theoretical groups were becoming

interested in the cooling, and some of the earlier work is discussed in

Letokhov, Minogin, and Pavlik (1977), Kazantsev (1978), and Stenholm

(1986).

To us, the cooling of course provided a start toward improving

clocks and in 1985, working with John Bollinger, John Prestage, and

Wayne Itano, we demonstrated the first clock that utilized laser cooling

(Bollinger e¢ al., 1985). But as physicists, we were excited by just the

cooling process itself. So, in addition to clock applications, it would

eventually lead to reaching and controlling the lowest quantized levels of

motion for a trapped particle (below).

Ill. Controlling the Quantum Levels of Individual Trapped Ions

One of the obvious next steps was to isolate single ions. In addition

to the aesthetic appeal of this, as for single electrons, the systematic errors

in spectroscopy would be smallest in this case (Dehmelt, 1982). By

observing steps in the ion laser fluorescence, the Heidelberg group was able

to isolate Ba’ single ions (Neuhauser ef a/., 1980). With Wayne Itano, we

subsequently used this fluorescence “steps” method to observe single

**Mg* ions (Wineland and Itano, 1981). The Heidelberg group also made

photographs of a single ion, and because of its relatively long fluorescence

wavelength (493 nm), with a magnifier, a single Ba’ ion can be observed

with the human eye!

In NIST single-ion experiments we chose to focus on Hg" because

for frequency-standard applications, '”” Hg* has a relatively high ground-

state hyperfine clock transition frequency of 40.5 GHz (Major and Werth,

1973; Cutler, Giffard, and McGuire, 1982; Prestage, Dick, and Maleki,

1991) and also anarrow *S,,—°D,, optical transition | c( * Dy ) = 86 ms |,

which could potentially be used as an optical frequency standard (Bender

et al., 1976). Although optical pumping of '” Hg* could be achieved with

radiation from isotopically selected Hg* fluorescence lamps (Major and

Werth, 1973; Cutler, Giffard, and McGuire, 1982; Prestage, Dick, and

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Maleki, 1991), laser excitation was made difficult because of the short

(194 nm) wavelength required. Jim Bergquist in our group, with

colleagues Hamid Hemmati and Wayne Itano, first developed the required

source by sum-frequency mixing a doubled Ar’ laser at 515 nm with 792

nm from a dye laser in a potassium pentaborate crystal (Hemmati,

Bergquist, and Itano, 1983). We used an rf trap with a simple ring-and-

end-cap structure shown in Fig. 1, similar to that used by the Heidelberg

group.

“optical clock” transition

counts >

Pry

Dsy2

Hg* 282 nm

S42

cooling

and detection

single Hg*

FIG. 1 (color). Schematic of the trap for single Hg” ion studies. An rf potential is applied

between the ring electrode and endcap electrodes (which are in common), forming an

rf “pseudopotential” for the ion. The relevant Hg” energy levels are indicated,

including the narrow *S,, *D,,, “optical clock” transition. The data in the upper

right-hand part of the figure show the number of 194 nm fluorescence photons

detected in 10 ms detection bins vs time when both transitions are excited

simultaneously (Bergquist ef a/., 1986).

By the mid-1980s ion trappers were able to directly address one of

Schrédinger’s questions, which formed the title for his publication “Are

there quantum jumps?” (Schrédinger, 1952a, 1952b). Three similar

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demonstrations were made in 1986 (Bergquist ef al., 1986; Nagourney,

Sandberg, and Dehmelt, 1986; Sauter e/ al., 1986; Blatt and Zoller, 1988);

for brevity, we describe the experiment of Bergquist ef al. Referring to

Fig. 1, anearly harmonic binding potential called a pseudopotential (Paul,

1990) is formed by applying an rf potential between the ring electrode

and the endcap electrodes (held in common). The relevant optical energy

levels of a Hg’ ion are indicated in the upper left-hand part ofthe figure. The

*S\. > °P,, electric-dipole transition E =194nm, T( 1B .| =2.9 ns | was

used for Doppler laser cooling. If continuously applied, a steady

fluorescence from the ion would be observed and could be used to

produce images of the ion. If *S,, > *D,, resonance radiation was

applied simultaneously, one would expect the 194 nm fluorescence to

decrease because of excitation to the “D,,, state.

A density-matrix description, valid for an ensemble of atoms,

would predict a reduced but steady fluorescence rate. But what would be

observed for a single 1on? (Cook and Kimble, 1985; Erber and Putterman,

1985; Cohen-Tannoudji and Dalibard, 1986; Javanainen, 1986; Kimble,

Cook, and Wells, 1986; Pegg, Loudon, and Knight, 1986; Schenzle, DeVoe,

and Brewer, 1986). In fact the 1on’s fluorescence does not steadily decrease,

but switches between the full value and no fluorescence, effectively

indicating quantum jumps between the *Si/2 and *Ds/2 states. For the data

shown in the upper right-hand corner of Fig. 1, the 194 nm fluorescence

photon counts registered by a photomultiplier tube were accumulated in

10 ms time bins and plotted as a function of elapsed time to show the jumps.

In amore general context, a measurement of the quantum system composed

of the 2Si2 and *Dsz2 states can be made by applying the 194 nm

‘“measurement’’ beam for 10 ms and observing the presence or absence of

fluorescence. The *S,, > *P,, transition is some-times called a “cycling

transition” because when the 71/2 state is excited to the 7P1/2 state, the ion

decays back to the *Si/2 state, emitting a photon, and the excitation/decay

process is then repeated. Neglecting the occasional decays of the *P1/2 to the

2132 state (Itano ef al., 1987), this procedure approximates an ideal

measurement in quantum mechanics because the detection of the state is

nearly 100% efficient and because the state of the Hg" ion, either the 7S/2 or

2Ds7. state, remains in its original condition after the measurement.

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Dehmelt dubbed this “electron shelving” detection (Dehmelt, 1982), where

in this example the ion is shelved to the *Ds/2 state. Such measurements are

also called quantum nondemolition (QND) measurements (Braginsky and

Khalili, 1996; Haroche and Raimond, 2006). The method of detection by

state-dependent fluorescence has now become rather ubiquitous in atomic

physics.

Frequency Detuning (in MHz)

— *D,, transition on a single '?*Hg* ion.

FIG. 2 (color). Spectroscopy of the *§

1/2

Referring to Fig. 1, for each measurement cycle, the ion is prepared in Sas =|L) state by

allowing it to decay to that level. Then, application of a 282 nm “probe” laser beam is

alternated with a 194 nm measurement beam. The I) and "Dia =|T) states are

detected with nearly 100% efficiency by observing the presence or absence of 194 nm

scattered light. By stepping the frequency of the probe beam and averaging over many

measurements, we obtain the spectrum shown where we plot the probability of the ion

remaining in the 7S}/2 state P(*S1/2) vs the 282 nm laser beam frequency. In a quantum

picture of the motion, the central feature or “carrier” state denotes transitions of the

form |)\n) > )|n), where 1 denotes the motional Fock state. “Red” and “blue”

aesands correspond to |) 72) >|7)|n+An) transitions with An = —-1 or +1,

respectively. The central feature or carrier is essentially unshifted by photon recoil, since

the recoil is absorbed by the entire trap apparatus as in the Mossbauer effect; see, e.g.,

Dicke (1953), Lipkin (1973), and Wineland ef a/. (1998).

To perform spectroscopy on the *S,,, > *D,, transition (A. ~ 282

nm), radiation was first applied near the transition frequency in the

absence of the 194 nm beam; this avoids perturbations of the energy levels

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from the 194 nm beam. The 282 nm beam was then switched off, followed

by measurement of the ion’s state with the 194 nm beam. This process

was repeated many times, and by stepping the frequency of the 282 nm

beam, spectra like that shown in Fig. 2 are obtained (Bergquist, Itano,

and Wineland, 1987). To interpret this spectrum, we must consider the

motion of the ion. Along any mode axis the motion is nearly harmonic, so

in the frame of the ion, the laser beam appears to be sinusoidally

frequency modulated due to the first-order Doppler shift. Thus the central

feature or “carrier,” which corresponds to the transition frequency, is

surrounded by frequency-modulation sidebands spaced by the motional

frequency of the ion (Dicke, 1953). An equivalent picture is that the ion can

absorb radiation while simultaneously gaining or losing one quantum of

motion, which leads to absorption features spaced by the frequency of

motion around the carrier.

As in many atomic physics experiments, by using highly coherent

radiation, we can initialize an ion in an eigenstate and deterministically

prepare superpositions; e.g., ) > a\l)+B \t). To extract the values of

| and | Bl, we detect as described above. A single measurement indicates

either the R or |) state with respective probabilities P = lal and 1-a/’.

Quantum fluctuations or “projection noise” in the measurements are

characterized with a variance ,/P(1—P)/M, where Mis the number of

measurements on identically prepared atoms (Itano ef a/., 1993). Therefore,

accurate measurements of P generally require many repeated experiments.

Similarly, Ramsey-type experiments where the two pulses are separated in

time can measure the relative phase between o and f. From these types of

measurements, many ion trap groups now routinely produce and verify

superposition states of single ions that have coherence times exceeding | s.

[For ion ensembles, coherence times exceeding 10 min have been

demonstrated (Bollinger e/ al., 1991; Fisk ef al., 1995).]

The Hg‘ clock project at NIST, led by Jim Bergquist, has been a

long but very successful story. First, an accurate clock based on the 40.5

GHz hyperfine transition of a few '’Hg" ions confined in a linear Paul trap

achieved systematic errors of about 4 x 10" (Berkeland ef al., 1998).

Although we felt these errors could be substantially reduced, we also

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realized that the future of high-performance clocks was in the optical

domain, so we focused on the *S,, > *D,,, optical clock transition. For

many years it had been appreciated that higher frequency was advantageous

in terms of measurement precision; basically the higher oscillation

frequencies allows one to divide a time interval into finer units. But two

things were needed: a laser with high enough spectral purity to take

advantage of narrow optical transitions, and a practical means to count

cycles of the “local oscillator,” in this case the laser that would excite the

clock transition. In our lab, Brent Young, Bergquist, and colleagues were

able to make a cavity-stabilized laser at 563 nm, which was doubled to

produce the clock radiation. The 563 nm source had a line- width of less

than 0.2 Hz for an averaging time of 20 s (Young ef al., 1999). It 1s now

understood that the linewidth was limited by thermal fluctuations in the

mirror surface, currently still the limit for the most stable lasers. The

solution to the second problem is by now well known. The relatively

rapid development of optical combs by Jan Hall (Hall, 2006), Ted Hansch

(Hansch, 2006), their colleagues, and other researchers meant that it was

now possible to effectively count optical cycles. Including these

developments, in 2006, Bergquist and colleagues demonstrated a '??Hg*

optical clock with a systematic uncertainty of 7.2 x 10°'’, the first clock

since the inception of atomic clocks that had smaller systematic errors than

a cesium clock (Oskay ef al., 2006).

IV. Manipulating Ion Motion at the Quantum Level

An interesting next step would be to control an ion’s motion at the

quantum level. Since a cold trapped 1on’s motion along any mode axis is

harmonic to a very good approximation, in a quantum description

. (Neuhauser ef al., 1978; Wineland and Itano, 1979; Stenholm,

1986), we express its Hamiltonian in the usual way as ha@.a'a with wz

the oscillation frequency (along the zaxis here) and a and a’ the lowering

and raising operators for the ion motion. The operator for the ion’s

position about its mean value is z=z, (a+a‘), where z, =,/h/2mq@._ is

the spread of the ground-state wave function, with m the ion’s mass. In

principle, we could detect the ion’s motion through the current it induces in

the trap electrodes, as was done for electrons. In practice, however, a far more

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sensitive method is to map information about the motional states onto internal

States of the ion and read those out as described above. For this, we need to

efficiently couple an ion’s internal states to its motion. To see how this

works, consider a single trapped ion that has a single-electron electric-dipole

transition with resonance frequency a. If this transition is excited by a laser

beam of frequency @. propagating along the z axis, the interaction is given

H, =—er-é€ E, cos(kz—@,t+@)

= AQ (o, On ) Ca ae priate) ;

(2)

where 7 is the electron coordinate relative to the ion’s core, e is the electron

charge, E€, Eo, and k are, respectively, the laser beam’s electric-field

polarization, amplitude, and wave vector, and @ is the electric-field phase at

the mean position of the ion. The operators o, (= xe ) and o_ (= Rare )

are the internal state raising and lowering operators, and

Oe ee, (17 E 1) / 2h, with RD and| il) denoting the 1on’s ground and

optically excited states as above. If we transform to an interaction picture for

the ion’s internal states (o, — Cue =) and motion states ( a’ > a'e’® s) and

assume @, = @,, then neglecting terms that oscillate near 2 Wo (rotating

wave approximation), Eq. (2) becomes

H, = = noe aa) ore

=fhQo.e —il (@, —Q t+] [1+in(ae Ot 4 ate mt) |-HLe (3)

Here, H.c. stands for Hermitian conjugate and 7 = kz, = 27z,/A is the

Lamb-Dicke parameter, which we assume here to be much less than 1. For an

@,/2% =3MHz and 2=729 nm, we have Z, = 6.5 nm and 7 =

0.056. For w, = @, and 72 << @, , to a good approximation we can

neglect the non-resonant 77 term in Eq. (3) and obtain H, =hQeS, +H.c.. This

is the Hamiltonian for carrier transitions or, equivalently, spin-vector rotations

about an axis in the x-y plane of the Bloch sphere. If we assume

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@, = @, — w, (laser tuned to the ‘‘red sideband’’), and absorb phase factors

in the definition of Q, the resonant term gives

H, =hn(Qo,a+Q"o_a"). (4)

This Hamiltonian describes the situation where a quantum of motion is

exchanged with a quantum of excitation of the ion’s internal state. It is

most commonly known as the Jaynes- Cummings Hamiltonian from

cavity QED, which expresses the exchange of energy between the internal

states of an atom in a cavity and the photons confined by the cavity (Jaynes

and Cummings, 1963; Haroche and Raimond, 2006). In the cavity-QED

experiments of Serge Haroche, Jean-Michel Raimond, Michel Brune, and

their colleagues in Paris, the atoms play much the same role as they do in

the ion experiments; however, in the cavity-QED experiments, the relevant

harmonic oscillator is that which describes a field mode of the cavity, whereas

in the ion case, the relevant harmonic oscillator is that associated with the

ion’s motion (Sauter ef al, 1988; Blockley, Walls, and Risken, 1992).

Over the years, this connection has led to some interesting and

complementary experiments between the two types of experiments

(Haroche and Raimond, 2006).

In the trapped-ion world, this type of exchange at the quantum level

was first used in the electron g-factor experiments of Dehmelt and

colleagues, where a change of the electron’s cyclotron quantum number

was accompanied by spin flip of the electron, which could be detected

indirectly (Dehmelt, 1990). If we apply Hi of Eq. (4) to an atomic ion in

the state ls) | n) , where n denotes the harmonic oscillator’s quantum state

(Fock state), we induce the transition |) |) >| )|n—1). This

corresponds to the absorption feature labeled An=—1 in Fig. 2, and

reduces the energy of motion by jw.. When the ion decays, on average, the

motion energy increases by the recoil energy

R=(hk) /(2m), where k=277/ A. Typically, we can achieve the

condition R<<hq@_, so that in the overall scattering process the

motional energy is reduced. In Fig. 2, the carrier absorption feature is

labeled An=0, indicating photon absorption without changing the

motional state. This is a manifestation of the “recoilless” absorption of the

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Méssbauer effect [see, e.g., Dicke (1953), Lipkin (1973), and Wineland ef

al. (1998)], but in the visible wavelength region.

Continuous application of the red-sideband transition provides a

relatively straightforward way to laser cool the ion to near the ground state

of motion. After many scattering events, the ion reaches the Raia =")

state, a “dark state” in which scattering stops, since the t)\7 =-1) state

does not exist. The process is not perfect, since scattering in the wings of

An = 0, +1 transitions leads to some residual recoil heating, but the

condition (n) <<l can be achieved. This is easily verified because

absorption on the An=—-1 red sideband nearly disappears, but the

An=+1 blue-sideband absorption remains. In 1989, with Frank

Diedrich, who was a postdoc in our lab, we achieved near-ground-state

laser cooling in two dimensions, in essentially the way described here

(Diedrich ef a/., 1989). Later in an experiment led by Chris Monroe, we

achieved near-ground-state cooling in 3D using two-photon stimulated-

Raman transitions (Monroe, Meekhof, King, Jefferts ef al., 1995).

In addition to suppressing Doppler shifts in spectroscopy to the

highest degree possible (Wineland ef al., 1987), one motivation for

sideband cooling was the intrinsic appeal of (actively) placing a bound

particle in its ground state of motion, the lowest energy possible within

the limitations imposed by quantum mechanics. Here, the ground state is

Gaussian-shaped wave packet with spread

Ie =,/h/2ma@, =z, and energy h@,/2. We were also interested in

Wied non-classical states of motion (Heinzen and Wineland, 1990;

Cirac, Blatt et al., 1993; Cirac, Parkins et al., 1993; Cirac et al., 1996) or

entangled states of spins (Wineland ef al., 1992; Bollinger et al., 1996).

For these experiments, cooling to the ground state of motion provides a

clean starting point for motional state manipulation. [In the Paris

experiments, the ground state of the cavity mode can be achieved either by

thermally cooling to (n) <<1 by operating at low temperature or by

extracting photons with atoms sent through the cavity in a process

analogous to ion sideband cooling (Haroche and Raimond, 2006). ]

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The red-sideband interaction of Eq. (4) and the “blue- sideband”

interaction (4, =hnQo,a'+H.c., for a, =a + o. ) that induces

| )|\n) = IT ))n+ 1) transitions, provide simple tools for the manipulation

of an ion’s motional states. For example, starting from lL )|n= 0) , and

applying a series of blue-sideband, red-sideband, and carrier 7 pulses, Fock

states for a selected value of n can be deterministically prepared (Meekhof

er al, 1996). From JL )|n = 0) , we can also make coherent states ion

motion by forcing the ion at its motion frequency with an oscillating

classical uniform field (Carruthers and Nieto, 1965) or by applying an

oscillating optical-dipole force (Meekhof e¢ a/., 1996), which results from

spatial gradients of laser-beam-induced ac Stark shifts. A coherent state of

a quantum particle 1s very much like an oscillating classical particle but,

as opposed to a classical particle that can be point-like, the shape of the

quantum particle’s wave packet 1s the same as it is in the ground state. In a

clever but straightforward scheme suggested by Chi Kwong Law and Joe

Eberly (Law and Eberly, 1996) arbitrary motional state superpositions can

be prepared (Ben-Kish ef a/., 2003). As a final example, the red-sideband

interaction applied for a “m-pulse” duration t=7/ (27782) provides

internal-state to motion-state transfer

(a|L)+B]T))|0) > \L)(ao)+ AI). )

V. Schrédinger’s Cat

The optical-dipole force is interesting because the strength of the

force can depend on the ion’s internal state. In 1996 (Monroe ef ai.,

1996), using state-dependent optical-dipole forces, we were able to

produce an analog to the Schrédinger’s cat state in Eq. (1), which had the

form

¥=—["Nla)+|YI-2)] 6

where |@) denotes a coherent state. The amplitude of the particle’s

oscillatory motion is equal to 2azo0. The spatial part of the state in Eq. (6)

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represents two wave packets that oscillate back and forth but are 180° out

of phase with each other and therefore pass through each other at the

center of the trap every half cycle of oscillation. Here, the analogy to

Schrédinger’s cat is that the spin states of the ion are like the states of the

single radioactive particle and the coherent states of the ion, which follow

more macroscopic classical trajectories, are like the state of the cat;

e.g., the ion at its left extremum point = live cat, ionat its right extremum

= dead cat. Figure 3 describes how this state was produced.

ENS ENV, ey ax

4 n/2) YY [7/2

by, NN VEN VINO NG GeO

(a) (b) (c) (d) (e) (f)

FIG. 3 (color). Depiction of the harmonic oscillator potential and the wave packets

for each component of the ion’s internal states, denoted i) and \). The images

are snapshots in time; for images (c) through (f) the wave packets are shown at the

extremes of their motion. The areas of the wave packets correspond to the probability of

finding the atom in the given internal state. (a) The initial wave packet corresponds to

the ground state of motion after laser cooling and preparation of the |) internal state.

(b) A m/2 carrier pulse creates the internal-state superposition sll4)+11) (c) An

oscillating optical-dipole force is applied that excites only the \t) component of the

F(lYle=9) +1") (d) The spin states are flipped by applying a carrier 7 pulse.

(e) The wave packet associated with the 1) state is excited by the optical-dipole force

to an amplitude of —@, that is, out of phase with respect to the first excitation.

This is the state of Eq. (6). (f) To analyze the state produced in step (e) and verify

phase coherence between the components of the cat wave function, we apply a final 1/2

carrier pulse and then measure the probability P(L) of the ion to be in state |) (see

text). From Monroe ef al., 1996.

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158

To analyze the experiment, in Fig. 3, we can control the phase of

the amplitude such that the coherent state is e’’a@ rather than —a. Near the

condition ¢ = 0 , the probability P(t) of the ion to be in state |) oscillates

as a function of ¢ due to interference of the two wave packets. This verifies

the coherence between the two components of the cat superposition state.

These interference oscillations are very analogous to the fringe oscillations

observed in Young’s-slit-type experiments performed on _ individual

photons, electrons, neutrons, or atoms, but in those experiments the

particle wave packets disperse in time, whereas the wave packets in a

harmonic oscillator do not, and 1n principle last arbitrarily long.

In Monroe ef al. (1996), for the condition described by Eq. (6), the

maximum separation of the wave packets was 4az, = 83 nm, while

the size of the wave packets zo was 7.1 nm [see also McDonnell ef al.

(2007) and Poschinger ef al. (2010)]. Of course, one might object to

dignifying the state produced by calling it a Schrédinger cat since it 1s

so small. In fact as we tried to make la larger, the quality of the

superposition became more susceptible to decoherence caused by noisy

ambient electric fields (Myatt ef al., 2000a, 2000b; Turchette ef al.,

2000), limiting the size that was obtained. However, as far as we know,

this 1s just a technical, not fundamental limitation and we should

eventually be able to make a cat with la| large enough that the wave

packets are separated by macroscopic distances.

VI. Enter Quantum Information

Following Peter Shor’s development of a quantum- mechanical

algorithm for efficient number factoring (Shor, 1994), there was a

dramatic increase of activity in the field of quantum information science.

The potential realization of general-purpose quantum information

processing (QIP) is now explored in many settings, including atomic,

condensed-matter, and optical systems.

At the 1994 International Conference on Atomic Physics held in

Boulder, Colorado, Artur Ekert presented a lecture outlining the ideas of

quantum computation (Ekert, 1995), a subject new to most of the audience.

This inspired Ignacio Cirac and Peter Zoller, who attended the conference

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and were very familiar with the capabilities (and limitations) of trapped- 1on

experiments, to propose a basic layout for a quantum computer utilizing

trapped ions (Cirac and Zoller, 1995). This seminal paper was the first

comprehensive proposal for how a quantum information processor might

be realized. In their scheme, quantum bits or ‘“‘qubits” are realized with two

internal states of the ion, e.g., the RD and I?) states above. The ion qubits

are held in a trap shown schematically in Fig. 4. The motion of the ions

is strongly coupled by the Coulomb

SPIN - MOTION

GATE BEAM

“\ SPIN - MOTION

QUBIT TRANSFER BEAM

2 1

FIG. 4 (color online). Scheme for quantum computation proposed by Cirac and Zoller

(Cirac and Zoller, 1995). Quadrupolar electrodes are configured to produce a linear array

of trapped-ion qubits (filled black circles). Two diagonally opposite rods support an rf

potential to realize a ponderomotive pseudopotential transverse to the trap’s (horizontal)

axis. Static potentials applied to the end segments of the electrodes confine ions along

the axis. Ideally, all motional modes are laser cooled to the ground state before logic

operations. The quantized modes of motion can be used as a data bus to share

information between the internal-state qubits of ions that are selected by focused laser

beams (see text).

interaction and is best described by the normal modes of a kind of

pseudomolecule. Typically, the motion of each mode is shared among

all the ions and can act as a data bus for transferring information between

ions. A single-qubit gate or rotation (the relatively easy part) is

implemented by applying a focused laser beam or beams onto that ion

and coherently driving a carrier transition as described above. The harder

part is to perform a logic gate between two selected ions. This can be

accomplished by first laser cooling all modes to the ground state. The

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internal qubit state of one ion is then transferred onto the qubit formed from

the ground and first excited state of a particular mode of motion (laser

beam | in Fig. 4), as indicated in Eq. (5). Laser beam 2 then performs a logic

gate between the (shared) motion qubit state and a second selected ion.

Since the second ion is generally in a superposition state, before the gate

operation is performed, the wave function for the spin and motional state

of the second qubit can be written as

a|L)|0)+ BL )|1)+€|T)|0)+¢|T)I1). One type of logic gate imparts a

minus sign to the \T)|a) component of the wave function by

coherently driving a 2M transition

I?) |) — |aux)|0) > | T)\1), where |aux) is a third “auxiliary” internal

component of the wave function realizes an entangling two- qubit “z-

phase” gate and is universal for computation. Finally, the initial transfer

step on the first 10n 1s reversed, restoring the motion to the ground state

and effectively having performed the logic gate between the internal qubit

states of the two laser-beam-selected ions. At NIST, since we had

recently achieved ground-state cooling with stimulated- Raman

transitions on hyperfine qubit states, we were able to quickly demonstrate

a universal gate between a hyperfine qubit and a motional mode qubit

(Monroe, Meekhof, King, Itano, and Wineland, 1995). The complete

Cirac-Zoller gate between two selected qubits was subsequently

demonstrated by the Innsbruck group, led by Rainer Blatt (Schmidt-Kaler

et al., 2003).

state of the ion (Cirac and Zoller, 1995). Flipping the sign of the IT)

More streamlined gates were subsequently devised in which

multiple ions are addressed simultaneously by the same laser beams

(Sorensen and Melmer, 1999, 2000; Solano, de Matos Filho, and Zagury,

1999; Milburn, Schneider, and James, 2000; Wang, Sorensen, and

Melmer, 2001). These gates also have the advantage that it is not

necessary to prepare all modes in the ground state; it is only necessary that

each ion is maintained well within the Lamb-Dicke regime

(2) a (A/ Vis i These “geometric” gates can be viewed as arising from

quantum phases that are acquired when a mode of the ions’ motion is

displaced in phase space around a closed path; the phases accumulated are

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proportional to the enclosed area in phase space. The different gates can be

viewed in a common framework, the main difference being whether or not

the forces act on the spin states in the z basis (eigenstates JLT) ) or in

] ig

1)), F(W)-e|1))

(Lee ef al., 2005). The forces required for the displacements are usually

implemented with optical-dipole forces as in the Schrédinger cat example.

Since the forces are state dependent, the differential geometric phases

generate entangling gates. Two-qubit phase gates have been implemented

in the z basis (Leibfried et al., 2003; Home et al., 2006) and in the x, y basis

(Sackett et al., 2000; Haljan et al., 2005; Benhelm ef al., 2008; Kim et al.,

2009). In the Innsbruck experiment of Benhelm ef al. (2008), a Bell state

with fidelity 0.993(1) was produced, setting a standard for all QIP

experiments. The use of single- and multiqubit gates has enabled the

demonstration of several ion-based QIP algorithms; see, for example, Blatt

and Wineland (2008) and Blatt and Roos (2012). At NIST most such

demonstrations were led by Didi Leibfried. Chris Monroe’s group at the

University of Maryland is leading efforts on an entirely different scheme

for ion entanglement generation based on performing joint measurements

on photons that are first entangled with 10n qubits (Moehring ef a/., 2007;

Olmschenk ef al., 2010; Monroe ef al., 2012). This scheme has the

advantage that the ions don’t have to be in the Lamb-Dicke regime, and it

also enables entanglement of widely separated qubits because of the relative

ease of transferring photons over large distances.

the x, y basis [eigenstates of the form ~=(|L)+e8

The basic elements of the Cirac-Zoller proposal are carried forward

in the different variations of trapped-ion QIP. This proposal rejuvenated

the field of trapped ions and today there are over 30 groups in the world

working on various aspects of quantum information processing. These

include groups at the University of Aarhus; Amherst College; University

of California, Berkeley; University of California, Los Angles; Duke

University; ETH Ziirich; University of Freiburg; Georgia Tech; Griffiths

University; Imperial College; University of Innsbruck; Lincoln

Laboratories; Mainz University; University of Hannover and PTB

(Germany); MIT; NIST (USA); NPL (UK); Osaka University; Oxford

University; Joint Quantum Institute at the University of Maryland;

Université de Paris; Saarland University (Saarbriicken); Sandia National

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Laboratory (USA); Siegen University; Simon Fraser University; National

University of Singapore; Sussex University; University of Sydney;

Tsinghua University; University of Ulm; University of Washington;

Wabash College; and the Weizmann Institute.

VI(a). Quantum Simulation

In the early 1980s, Richard Feynman proposed that one quantum

system might be used to efficiently simulate the dynamics of other

quantum systems of interest (Feynman, 1982; Lloyd, 1996). This is now

a highly anticipated application of QIP and will likely occur well before

useful factorization is performed. Of course, the universality of a large-

scale quantum computer will allow it to simulate any quantum system of

interest. However, it is also possible to use the built-in available interactions

in a quantum processor to simulate certain classes of physical problems.

For trapped ions, it has been possible to use the interactions employed in

the various gates to simulate other systems of interest, for example,

nonlinear optical systems (Leibfried ef al., 2002), motional quantum

dynamics as in an electron’s Zitterbewegung (Gerritsma ef al., 2010), or

the properties of a ““quantum walk”? (Schmitz, Matjeschk ef al., 2009;

Zahringer ef al., 2010). Currently, efforts are underway in several

laboratories to use QIP interactions to simulate various dynamics including

those of condensed-matter systems. Some of the basic ideas for how this

might work with ions have been outlined in Wunderlich and Balzer (2003),

Porras and Cirac (2004, 2006), Deng, Porras, and Cirac (2005), Pons ef

al. (2007), Schatz et al. (2007), Chiaverini and Lybarger (2008), Taylor

and Calarco (2008), Clark et al. (2009), Johanning, Varon, and

Wunderlich (2009), Schmitz, Friedenauer ef al. (2009), Schmied,

Wesenberg, and Leibfried (2011), Blatt and Roos (2012), Britton er al.

(2012), Korenblit er al. (2012), and Schneider, Porras, and Schaetz (2012).

Here, logic gate interactions between ions 7 andj invoke a spin-spin—like

interaction of the form 0.,0,, where v7€ {X, W as Spin rotations about a

direction zw act like magnetic fields along w. These basic interactions have

been implemented on up to 16 ions in an rf trap (Schatz et al., 2007;

Friedenauer ef al., 2008; Kim ef al., 2009, 2010; Edwards et al., 2010;

Islam ef al., 2012; Korenblit ef a/., 2012). One interesting aspect of this

work is the study of quantum phase transitions by varying the relative

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strengths of the (simulated) spin-spin and magnetic field interactions.

Under appropriate conditions, the effects of spin “frustration” are now

becoming apparent. The basic interactions have also been implemented on

over 100 spins in a Penning trap experiment led by John Bollinger at NIST

(Britton e al., 2012), where the ions naturally form into a triangular array.

In the Innsbruck group, simulations including engineered dissipation have

also been implemented (Barreiro e/ al., 2011; Blatt and Roos, 2012), and a

striking demonstration of a digital quantum simulator has been made

(Lanyon ef al., 2011; Blatt and Roos, 2012), in essence the first universal

quantum computer.

VI(b). Spectroscopy and Quantum Metrology

Some potential applications of quantum control and QIP are

motivated by the idea of using entangled states to improve spectroscopic

sensitivity (Wineland ef al., 1992, 1994; Bollinger et al., 1996;

Leibfried ef al., 2004; Roos eft al., 2006; Goldstein et al., 2009) and

demonstrations of this increased sensitivity have been made (Meyer ef

al., 2001; Leibfried et al., 2004, 2005; Roos et al., 2006; Leroux, Schleier-

Smith, and Vuletic, 2010; Monz ef al., 2011). These demonstrations were

made in the limit that noise was dominated by “projection noise,’ the

fundamental noise arising from the fluctuations in which state the

system is projected into upon measurement (Wineland ef al., 1982;

Itano ef al., 1993). This might be the case in a spectroscopy experiment

where the interrogation time is limited by a particular experimental

constraint, like the duration of flight of atoms in a cesium fountain clock

or by the desire to hold the temperature of ions below a certain value

if they are heated during interrogation. However, if significant phase

noise is present in either the atoms themselves (Huelga ef al., 1997) or

the interrogating radiation (Wineland ef al., 1998; Buzek, Derka, and

Massar, 1999; André, Sorensen, and Lukin, 2004; Rosenband, 2012), the

gain from entanglement can be lost. This puts a premium on finding probe

oscillators that are stable enough that the projection noise dominates for

the desired probe duration.

Some ions of spectroscopic interest may be difficult to detect

because they either don’t have a cycling transition or lack a cycling

transition at a convenient wavelength. In some cases, this limitation can

be overcome by simultaneously storing the ion(s) of spectroscopic interest

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with a “logic” ion or ions whose states can be more easily detected.

Following the Cirac and Zoller scheme, we can use the internal-to-

motion-state-transfer process described above. Here, the idea is to first

transfer the two states of interest in the spectroscopy ion to the ground

and first excited states of a mode of the ions’ coupled motion. This 1s

then followed by mapping the motional states onto the logic 1on, which

is subsequently measured (Wineland ef al., 2002). In a project led by Till

Rosenband at NIST, this technique has been used to detect optical

transitions in ?7Al* ions by transferring the relevant 7’AI’ states to a ’Be*

or *°Mg' logic ion, which is then measured (Schmidt ef al., 2005). It is

now used routinely in an accurate optical clock based on 7/AI’

(Rosenband ef al., 2008; Chou, Hume, Koelemei ef a/., 2010) and might

also be extended to molecular ions. Currently, the *’Al’ single-ion optical

clock has the smallest systematic error of any clock at somewhat below

1 part in 10!’ (Chou, Hume, Koelemeij et al., 2010). This level of

precision has enabled observations of the predictions of Euinstein’s

general theory of relativity on a human scale, such as time dilation for

bicycling speeds and the gravitational redshift for height changes of

around 30 cm (Chou, Hume, Rosenband, and Wineland, 2010). Such

clocks may become useful tools in geodesy.

The information transfer and readout process employed in the

°7A1'/?Be* clock experiments typically had a fidelity of about 0.85, limited

by errors caused by the ions’ thermal motion in modes not used for

information transfer [so-called “Debye-Waller” factors from Méssbauer

spectroscopy (Lipkin, 1973; Wineland ef al., 1998)]. However, the

quantum logic detection process is a QND type of measurement in that it

doesn’t disturb the detected populations of the 77Al* ion. It can therefore

be repeated to gain better information on the *’Al’ ion’s (projected) state.

By use of real-time Bayesian analysis on successive detection cycles, the

readout fidelity was improved from 0.85 to 0.9994 (Hume, Rosenband,

and Wineland, 2007). This experiment shares similarities with those of

the Paris cavity- QED group, where successive probe atoms are used to

perform QND measurements of the photon number in a cavity (Deléglise

et al., 2008). In Hume, Rosenband, and Wineland (2007), the same atom

("Be’) is reset after each detection cycle and used again. Also, because

the detection was accomplished in real time, the procedure was adaptive,

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requiring on each run a minimum number of detection cycles to reach a

certain measurement fidelity.

Vil. Summary

[ have tried to give a brief account of some of the developments that

have taken place in the area of quantum state manipulation of small

numbers of trapped atomic ions. With apologies, I have omitted several

aspects of this subject and for the topics discussed here, I primarily used

examples from the NIST, Boulder group. Much of the other work has

been discussed in various comprehensive articles and reviews; see, for

example, Cirac et al. (1996), Wineland et al. (1998), Sasura and Buzek

(2002), Leibfried, Blatt, Monroe, and Wineland (2003), Lee ef al. (2005),

Blatt and Wineland (2008), Duan and Monroe (2008, 2010), Haffner,

Roos, and Blatt (2008), Kielpinski (2008), Monroe and Lukin (2008),

Blatt and Roos (2012), Korenblit et al. (2012), Monroe ef al. (2012),

and Schneider, Porras, and Schaetz (2012). Reviews on advanced clocks

including those based on ions are contained in Gill (2005, 2011), Maleki

(2008), and Margolis (2009) [see also Made] ef al. (2012) and references

therein].

Acknowledgments

Certainly my role in this work 1s very small when compared to that

of my colleagues both at NIST and around the world, who have made so

many important contributions. Having been recognized by the Royal

Swedish Academy of Sciences is really more recognition of our field

rather than individual accomplishment; many others are at least as

deserving. Just the work of the NIST group was due to the combined

efforts of a very large number of people. I have been lucky to work with

NIST permanent staff members Jim Bergquist, John Bollinger, Bob

Drullinger, and Wayne Itano for my entire career, and we have been

fortunate to be joined by Didi Leibfried and Till Rosenband in the last

decade. Chris Monroe was a very important part of our group from

1992 to 2000 and now has his own group at the University of Maryland.

Of course our successes would not have happened if not for the dedication

of many students, postdocs, and visiting scientists to our group,

numbering over 100 people. Having a group working directly together or

on related problems has been a source of strength for us, and the congenial

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atmosphere over the years has made our efforts so enjoyable. Throughout

my career, our group has enjoyed the support and encouragement of

NBS/NIST management. My direct supervisors over the years, Helmut

Hellwig, Sam Stein, Don Sullivan, and Tom O’Brian, have always

supported our goals and desires as much as possible. More recently, we

have also enjoyed the support of Carl Williams, who heads NIST’s

quantum information program. We are all indebted to our laboratory

director, Katharine Gebbie, for her support and encouragement.

Perhaps one measure of her success is that I am the fourth person, after

Bill Phillips, Eric Cornell, and Jan Hall, to receive a Nobel Prize during

her tenure as lab director. We are also grateful for the support of agencies

outside of NIST, such as AFOSR, ARO, DARPA, ONR, and various

intelligence agencies who have supported our work on quantum

information. I have great respect for the leaders of some of our group’s

strongest competition such as Rainer Blatt (Innsbruck) and Chris

Monroe (University of Maryland) and have enjoyed their friendship for

many years. It was also a great pleasure to share this recognition with

Serge Haroche. I have known Serge for about 25 years and have

enjoyed both his group’s elegant science and also the mutual friendship

that my wife and I have shared with him and his wife, Claudine. Most

importantly, I have been very fortunate to have the support, understanding,

and patience of my wife Sedna and sons Charles and Michael. I thank John

Bollinger, Wayne Itano, Didi Leibfried, and Till Rosenband for helpful

suggestions on the manuscript.

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JORDANA, ROMAN DE VICENTE (Dr.) Batalla De Garellano, 15, Aravaca, 28023,

Madrid, Spain (EF)

KAHN, ROBERT E. (Dr.) 909 Lynton Place, Mclean VA 22102 (F)

KARAM, LISA (Dr.) 8105 Plum Creek Drive, Gaithersburg MD 20882-4446 (F)

KATZ, ROBERT (Dr.) 3310 N. Leisure Blvd #530, Silver Spring MD 20906 (EF)

KAUFHOLD, JOHN (Dr.) Suite 1200, 4601 N. Fairfax Dr, Arlington VA 22203 (M)

KAY, PEG (Ms.) 6111 Wooten Drive, Falls Church VA 22044 (LF)

KEEFER, LARRY (Dr.) 7016 River Road, Bethesda MD 20817 (EF)

KEISER, BERNHARD E. (Dr.) 2046 Carrhill Road, Vienna VA 22181-2917 (LF)

KLINGSBERG, CYRUS (Dr.) Apt. L184, 500 E. Marylyn Ave, State College PA 16801-

6225 (EF)

KLOPFENSTEIN, REX C. (Mr.) 4224 Worcester Dr., Fairfax VA 22032-1140 (LF)

KRUEGER, GERALD P. (Dr.) Krueger Ergonomics Consultants, 4105 Komes Court,

Alexandria VA 22306-1252 (EF)

LAWSON, ROGER H. (Dr.) 10613 Steamboat Landing, Columbia MD 21044 (EF)

LEIBOWITZ, LAWRENCE M. (Dr.) 3903 Laro Court, Fairfax VA 22031-3256 (LF)

LEMKIN, PETER (Dr.) 148 Keeneland Circle, North Potomac MD 20878 (EM)

LESHUK, RICHARD (Mr) 9004 Paddock Lane, Potomac MD 20854 (M)

LEWIS, DAVID C. (Dr.) 27 Bolling Circle, Palmyra VA 22963 (F)

LEWIS, E. NEIL (Dr.) Malvern Instruments, Suite 300, 7221 Lee Deforest Dr, Columbia

MD 21046 (M)

LIBELO, LOUIS F. (Dr.) 9413 Bulls Run Parkway, Bethesda MD 20817 (LF)

LONDON, MARILYN (Ms.) 3520 Nimitz Rd, Kensington MD 20895 (F)

LONGSTRETH, II, WALLACE I (Mr.) 8709 Humming Bird Court, Laurel MD 20723-

1254 (M)

LOOMIS, TOM H. W. (Mr.) 11502 Allview Dr., Beltsville MD 20705 (EM)

LUTZ, ROBERT J. (Dr.) 6031 Willow Glen Dr, Wilminton NC 28412 (EF)

LYONS, JOHN W. (Dr.) 7430 Woodville Road, Mt. Airy MD 21771 (EF)

MALCOM, SHIRLEY M. (Dr.) 12901 Wexford Park, Clarksville MD 21029-1401 (F)

MANDERSCHEID, RONALD W. (Dr.) 10837 Admirals Way, Potomac MD 20854-

1232 (CF)

MARRETT, CORA (Dr.) 7517 Farmington Way, Madison WI 53717 (EF)

MENZER, ROBERT E. (Dr.) 90 Highpoint Dr, Gulf Breeze FL 32561-4014 (EF)

MESSINA, CARLA G. (Mrs.) 9800 Marquette Drive, Bethesda MD 20817 (EF)

METAILIE, GEORGES C. (DR.) 18 Rue Liancourt, 75014 Paris, FRANCE (F)

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178

MILLER, JAY H. (Mr.) 8924 Ridge Place, Bethesda MD 20817-3364 (M)

MILLER IH, ROBERT D. (Dr.) The Catholic University of America, 10918 Dresden

Drive, Beltsville MD 20705 (M)

MORGOUNOV, ALEXEY (Dr.) CIMMYT, P.K. 39, Emek, Ankara 06511, Turkey (M)

MORRIS, JOSEPH (Mr.) PO Box 3005, Oakton VA 22124-9005 (M)

MORRIS, P.E., ALAN (Dr.) 4550 N. Park Ave. #104, Chevy Chase MD 20815 (EF)

MOUNTAIN, RAYMOND D. (Dr.) 701 King Farm Blvd #327, Rockville MD 20850

(F)

MUELLER, TROY J. (Dr.) 42476 Londontown Terrace, South Riding VA 20152 (M)

MUMMA, MICHAEL J. (Dr.) 210 Glen Oban Drive, Arnold MD 21012 (F)

MURDOCH, WALLACE P. (Dr.) 65 Magaw Avenue, Carlisle PA 17015 (EF)

NORRIS, KARL H. (Mr.) 11204 Montgomery Road, Beltsville MD 20705 (EF)

O'HARE, JOHN J. (Dr.) 108 Rutland Blvd, West Palm Beach FL 33405-5057 (EF)

OHRINGER, LEE (Mr.) 5014 Rodman Road, Bethesda MD 20816 (EF)

ORDWAY, FRED (Dr.) 5205 Elsmere Avenue, Bethesda MD 20814-5732 (EF)

OTT, WILLIAM R (Dr.) 19125 N. Pike CreekPlace, Montgomery Village MD 20886

(EF)

PAJER, BERNADETTE (Mrs.) 25116 143rd St. SE, Monroe WA 98272 (M)

PARR, ALBERT C (Dr.) 2656 SW Eastwood Avenue, Gresham OR 97080-9477 (F)

PAULONIS, JOHN J (Mr.) P.O. Box 335, Yonkers NY 10710 (M)

PAZ, ELVIRA L. (Dr.) 172 Cook Hill Road, Wallingford CT 06492 (LEF)

PICKHOLTZ, RAYMOND L. (Dr.) 3613 Glenbrook Road, Fairfax VA 22031-3210

(EF)

POLAVARAPU, MURTY 10416 Hunter Ridge Dr., Oakton VA 22124 (LF)

POLINSKI, ROMUALD (Prof, Doctor of Sciences (Economics)) Ul. Generala Bora

39/87, 03-982 WARSZAWA 131, Poland (M)

PRZYTYCKI, JOZEF M. (Prof.) 10005 Broad St, Bethesda MD 20814 (F)

PYKE, JR, THOMAS N. (Mr.) 4887 N. 35th Road, Arlington VA 22207 (EF)

RADER, CHARLES A. (Mr.) 1101 Paca Drive, Edgewater MD 21037 (EF)

RAVITSKY, CHARLES (Mr.) 37129 Village 37, Camarillo CA 93012 (EF)

REAGAN, ANN M. (Dr.) PO Box 22, Lusby MD 20657 (M)

REISCHAUER, ROBERT (Dr.) 5509 Mohican Rd, Bethesda MD 20816 (EF)

RICKER, RICHARD (Dr.) 12809 Talley Ln, Darnestown MD 20878-6108 (F)

RIDGELL, MARY P.O. Box 133, 48073 Mattapany Road, St. Mary's City MD 20686-

0133 (LM)

ROBERTS, SUSAN (Dr.) Ocean Studies Board, Keck 607, National Research Council,

500 Fifth Street, NW, Washington DC 20001 (F)

ROGERS, KENNETH (Dr.) 355 Fellowship Circle, Gaithersburg MD 20877 (LM)

ROMAN, NANCY GRACE (Dr.) 8100 Connecticut Ave. Apt.1605, Chevy Chase MD

20815 (M)

ROOD, SALLY A (Dr.) PO Box 12093, Arlington VA 22219 (F)

ROSENBLATT, JOAN R. (Dr.) 701 King Farm Blvd, Apt 630, Rockville MD 20850

(EF)

SATTERFIELD, MARY (Dr.) 503 Main St. Apt 426, Gaithersburg MD 20878 (F)

SCHINDLER, ALBERT I. (Dr.) 6615 Sulky Lane, Rockville MD 20852 (EF)

SCHMEIDLER, NEAL F. (Mr.) 7218 Hadlow Drive, Springfield VA 22152 (F)

SCHNEPFE, MARIAN M. (Dr.) Potomac Towers, Apt. 640, 2001 N. Adams Street,

Arlington VA 22201 (EF)

Washington Academy of Sciences

SERPAN, CHARLES Z (Mr.) 5510 Bradley Blvd, Bethesda MD 20814 (M)

SEVERINSKY, ALEX J. (Dr) 4707 Foxhall Cres NW, Washington DC 20007-1064

(EM)

SHETLER, STANWYN G. (Dr.) 142 E Meadowland Ln, Sterling VA 20164-1144 (EF)

SHROPSHIRE, JR, W. (Dr.) Apt. 426, 300 Westminster Canterbury Dr., Winchester VA

22603 (LF)

SIMMS, JAMES ROBERT (Mr.) 9405 Elizabeth Ct., Fulton MD 20759 (M)

SMITH, THOMAS E. (Dr.) 3148 Gracefield Rd Apt 215, Silver Spring MD 20904-5863

(LF)

SNIECKUS, MARY (Ms) 1700, Dublin Dr., Silver Spring MD 20902 (F)

SODERBERG, DAVID L. (Mr.) 403 West Side Dr. Apt. 102, Gaithersburg MD 20878

(EM)

SOLAND, RICHARD M. (Dr.) 2516 Arizona Ave. Apt 6, Santa Monica CA 90404-1426

(LF)

SOZER, AMANDA (Dr.) 525 Wythe Street, Alexandria VA 22314 (M)

SPARGO, WILLIAM J. (Dr.) 9610 Cedar Lane, Bethesda MD 20814 (F)

SPILHAUS, JR, A.F. (Dr.) 10900 Picasso Lane, Potomac MD 20854 (EM)

SRIRAM, RAM DUVVURU (Dr.) 10320 Castlefield Street, Ellicott City MD 21042

(LF)

STERN, KURT H. (Dr.) 103 Grant Avenue, Takoma Park MD 20912-4328 (EF)

STEWART, PETER (Prof.) 417 7th Street NE, Washington DC 20002 (M)

STIEF, LOUIS J. (Dr.) 332 N St., SW., Washington DC 20024-2904 (EF)

STOMBLER, ROBIN (Ms.) Auburn Health Strategies, 3519 South Four Mile Run Dr.,

Arlington VA 22206 (M)

SYED, ALI (Dr) 603, H Street SW, Washington DC 20024 (M)

TABOR, HERBERT (Dr.) NIDDK, LBP, Bldg. 8, Rm 223, National Institutes of Health,

Bethesda MD 20892-0830 (M)

TEICH, ALBERT H. (Dr.) PO Box 309, Garrett Park MD 20896 (EF)

THEOFANOS, MARY FRANCES (Ms.) 7241 Antares Drive, Gaithersburg MD 20879

(M)

THOMPSON, CHRISTIAN F. (Dr.) 278 Palm Island Way, Ponte Vedra FL 32081 (LF)

TIMASHEV, SVIATOSLAV (SLAVA) A. (Dr.) 3306 Potterton Dr., Falls Church VA

22044-1603 (F)

TOUWAIDE, ALAIN Unit 405, 1423 R Street NW, Washington DC 20009 (LF)

TROXLER, G.W. (Dr.) PO Box 1144, Chincoteague VA 23336-9144 (F)

UMPLEBY, STUART (Professor) Apt 1207, 4141 N Henderson Rd, Arlington VA

22203 (EF)

VAISHNAV, P. P.O. Box 2129, Gaithersburg MD 20879 (LF)

VARADIL, PETER F. (Dr.) Apartment 1606W, 4620 North Park Avenue, Chevy Chase

MD 20815-7507 (EF)

VAVRICK, DANIEL J. (Dr.) 10314 Kupperton Court, Fredricksburg VA 22408 (F)

VOORHEES, ELLEN (Dr.) 100 Bureau Dr., Stop 8940, Gaithersburg MD 20899-8940

ees THOMAS A. (Dr.) 3910 Rickover Road, Silver Spring MD 20902 (F)

WEBB, RALPH E. (Dr.) 21-P Ridge Road, Greenbelt MD 20770 (EF)

WEIL, TIMOTHY (Mr.) SECURITYFEEDS, PO Box 18385, Denver CO 80218 (M)

WEISS, ARMAND B. (Dr.) 6516 Truman Lane, Falls Church VA 22043 (LF)

WERGIN, WILLIAM P. (Dr.) 1 Arch Place #322, Gaithersburg MD 20878 (EF)

Winter 2016

180

WHITE, CARTER (Dr.) 12160 Forest Hill Rd, Waynesboro PA 17268 (EF)

WIESE, WOLFGANG L. (Dr.) 8229 Stone Trail Drive, Bethesda MD 20817 (EF)

WILLIAMS, CARL (Dr.) 2272 Dunster Lane, Potomac MD 29854 (F)

WILLIAMS, E. EUGENE (Dr.) Dept. of Biological Sciences, Salisbury University, 1101

Camden Ave, Salisbury MD 21801 (M)

WILLIAMS, JACK (Mr.) 6022 Hardwick Place, Falls Church VA 22041 (F)

WITHERSPOON, F. DOUGLAS ASTI, 11316 Smoke Rise Ct., Fairfax Station VA

22039 (M)

WU, KELI (Mr.) 360, Suite 48, Swift Ave, South San Francisco CA 94080 (M)

Washington Academy of Sciences

182

Delegates to the Washington Academy of Sciences

Representing Affiliated Scientific Societies

Acoustical Society of America

American/International Association of Dental Research

American Association of Physics Teachers, Chesapeake

Section

American Astronomical Society

American Fisheries Society

American Institute of Aeronautics and Astronautics

American Institute of Mining, Metallurgy & Exploration

American Meteorological Society

American Nuclear Society

American Phytopathological Society

American Society for Cybernetics

American Society for Microbiology

American Society of Civil Engineers

American Society of Mechanical Engineers

American Society of Plant Physiology

Anthropological Society of Washington

ASM International

Association for Women in Science

Association for Computing Machinery

Association for Science, Technology, and Innovation

Association of Information Technology Professionals

Biological Society of Washington

Botanical Society of Washington

Capital Area Food Protection Association

Chemical Society of Washington

District of Columbia Institute of Chemists

District of Columbia Psychology Association

Eastern Sociological Society

Electrochemical Society

Entomological Society of Washington

Geological Society of Washington

Historical Society of Washington DC

Human Factors and Ergonomics Society

(continued on next page)

Paul Arveson

J. Terrell Hoffeld

Frank R. Haig, S. J.

Sethanne Howard

Lee Benaka

David W. Brandt

E. Lee Bray

Vacant

Charles Martin

Vacant

Stuart Umpleby

Vacant

Daniel J. Vavrick

Mark Holland

Vacant

Toni Marechaux

Jodi Wesemann

Vacant

F. Douglas

Witherspoon

Vacant

Chris Puttock

Keith Lempel

Vacant

Ronald W.

Mandersheid

Vacant

Jeff Plescia

Jurate Landwehr

Vacant

Gerald Krueger

Washington Academy of Sciences

Delegates to the Washington Academy of Sciences

Representing Affiliated Scientific Societies

(continued from previous page)

Institute of Electrical and Electronics Engineers, Washington

Section

Institute of Food Technologies, Washington DC Section

Institute of Industrial Engineers, National Capital Chapter

International Association for Dental Research, American

Section

International Society for the Systems Sciences

International Society of Automation, Baltimore Washington

Section

Instrument Society of America

Marine Technology Society

Maryland Native Plant Society

Mathematical Association of America, Maryland-District of

Columbia-Virginia Section

Medical Society of the District of Columbia

National Capital Area Skeptics

National Capital Astronomers

National Geographic Society

Optical Society of America, National Capital Section

Pest Science Society of America

Philosophical Society of Washington

Society for Experimental Biology and Medicine

Society of American Foresters, National Capital Society

Society of American Military Engineers, Washington DC

Post

Society of Manufacturing Engineers, Washington DC

Chapter

Society of Mining, Metallurgy, and Exploration, Inc.,

Washington DC Section

Soil and Water Conservation Society, National Capital

Chapter

Technology Transfer Society, Washington Area Chapter

Virginia Native Plant Society, Potowmack Chapter

Washington DC Chapter of the Institute for Operations

Research and the Management Sciences (WINFORMS)

Washington Evolutionary Systems Society

Washington History of Science Club

Washington Paint Technology Group

Washington Society of Engineers

Washington Society for the History of Medicine

Washington Statistical Society

World Future Society, National Capital Region Chapter

Richard Hill

Vacant

Neal F. Schmeidler

J. Terrell Hoffeld

Vacant

Hank Hegner

Jake Sobin

Vacant

D.S. Joseph

Vacant

Jay H. Miller

Vacant

James Cole

Vacant

Eugenie Mielczarek

Vacant

Daina Apple

Vacant

BE. Lee Bray

Terrell Erickson

Richard Leshuk

Vacant

Russell Wooten

Vacant

Albert G. Gluckman

Vacant

Alvin Reiner

Alain Touwaide

Michael P. Cohen

Jim Honig