New Mechanisms for Laser CoolingClaude N. CohenTannoudji and William D. Phillips Citation: Phys. Today 43(10), 33 (1990); doi: 10.1063/1.881239 View online: http://dx.doi.org/10.1063/1.881239 View Table of Contents: http://www.physicstoday.org/resource/1/PHTOAD/v43/i10 Published by the American Institute of Physics. Additional resources for Physics TodayHomepage: http://www.physicstoday.org/ Information: http://www.physicstoday.org/about_us Daily Edition: http://www.physicstoday.org/daily_edition

NEW MECHANISMSFOR LASER COOLING

Optical pumping and light shifts haveunexpectedly conspired to improve

loser cooling by orders of magnitudeand to produce the lowest kinetic

temperatures ever measured.

Claude N. Cohen-Tannoudjiand William D. Phillips

Claude Cohen-Tannoudji is a professor at ihe College deFrance and does research at the Ecole Normale Superieure ina laboratory associated with the University of Paris VI andwith Centre National de la Recherche Scientifique.William Phillips is a physicist at the National Institute ofStandards and Technology (formerly the National Bureau ofStandards) in Caithersburg, Maryland.

When an atom or a molecule interacts with a light beam,the light emitted or absorbed carries valuable informationabout the atomic or molecular structure. This phenome-non underlies the whole field of spectroscopy. But theinteraction of a photon with an atom can be used tomanipulate the atom as well as to probe its structure. Forexample, in an approach called optical pumping, inventedby Alfred Kastler, one can use the resonant exchange ofangular momentum between atoms and polarized photonsto align or orient the spins of atoms or to put them in non-equilibrium situations. In his original 1950 paper Kastleralso proposed using optical pumping to cool and to heat theinternal degrees of freedom, calling the phenomena the"effet luminofrigorique" and the "effet luminocalorique."Another famous example of the use of photon-atominteraction to control atoms is laser cooling. This tech-nique relies on resonant exchange of linear momentumbetween photons and atoms to control their externaldegrees of freedom and thus to reduce their kinetic energy.Laser cooling was suggested independently by TheodorHansch and Arthur Schawlow for neutral atoms' and byDavid Wineland and Hans Dehmelt for trapped ions.2 Inan article written three years ago for PHYSICS TODAY (June1987, page 34), Wineland and Wayne Itano presented theprinciple of laser cooling and the potential applications ofcold atoms to fields of physics such as ultrahigh resolutionspectroscopy, atomic clocks, collisions, surface physics andcollective quantum effects. At that time laser cooling hadbrought temperatures down to a few hundred microkelvin,but unexpected improvements during the last three yearshave dramatically lowered those temperatures to only afew microkelvin. We now feel we understand the newphysical mechanisms responsible for these very lowtemperatures.

Doppler cooling: The traditional mechanismThe principle of Doppler cooling for free atoms' can best beillustrated by a two-level atom in a weak laser standingwave with a frequency w, slightly detuned below theatomic resonance frequency wA (see figure la). Each ofthe two counterpropagating laser beams forming thestanding wave imparts an average pressure in its directionof propagation as the atom absorbs photons in thatdirection but radiates the photons isotropically. Supposefirst that the atom is at rest. The radiation pressuresexerted by the two counterpropagating waves exactlybalance, and the total force experienced by the atom,averaged over a wavelength, vanishes. If the atom ismoving along the standing wave at velocity v, thecounterpropagating waves undergo opposite Dopplershifts + io] i'/c = ± kv, where k is the magnitude of thewavevector. The frequency of the wave traveling oppositeto the atom gets closer to resonance and this wave exerts astronger radiation pressure on the atom than the wavetraveling in the same direction as the atom, which getsfarther from resonance. This imbalance between the two

ft) 1990 American Instirure ol Physics PHYSICS TODAY OCTOBER, 1990 3 3

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radiation pressures gives rise to an average net frictionforce F, which is opposite to the atomic velocity v andwhich can be written, if v is low enough, as F= — av,where a is a friction coefficient.

Figure lb shows, for low laser intensity 7L, thedamping (cooling) force as the sum of two opposing forcesthat vary with kv as Lorentzian curves, each curve havinga width F equal to the natural width of the excited state.These curves are centered at kv = + 8, whereS = (jL — wA is the amount by which the frequency isdetuned from resonance. The slope of the total force atv = 0, that is, the friction coefficient a, is maximum whenS~ — F/2. The total force is then proportional to thelaser intensity, always opposes the velocity and is nearlylinear in velocity for \kv\ < F/2. This inequality defines arange vD of velocities (called the velocity capturerange) over which the atomic motion is most effectivelydamped by Doppler cooling. For low /, this range isindependent of IL.

Actually, the friction force considered above is only amean force, averaged over several fluorescence cycles.The random nature of radiative processes introducesfluctuations in atomic motion. For example, each indi-vidual fluorescence photon is emitted in a randomdirection, giving a random recoil to the atom. Further-more, the number of fluorescence cycles occurring duringa given time interval is random, so that the momentumabsorbed from the laser beams by the atom during thistime interval is also random. As in Brownian motion,these fluctuations in momentum exchanges tend toincrease the width Ap of the atomic momentum distribu-tion. The corresponding heating rate is characterized bythe rate of increase of (Ap)2, that is, by the momentumdiffusion coefficient D, which can be shown to be propor-tional to the laser intensity /, . In the steady state theheating rate, characterized by D, is balanced by thecooling rate, characterized by the friction coefficient a,and the atom reaches an equilibrium temperature T thatis proportional to D/a. Since both D and a are propor-tional to the laser intensity IL, T is predicted to beindependent of /, (in the limit of low 7L). From thetheoretical expressions for D and a, one can show1 thatthe lowest temperature TD that can be achieved byDoppler cooling is given by kH Tu = -fir/2. This "Dopplerlimit" is obtained for a frequency detuning of 8 = — 172.For sodium, TD is approximately 240 /JK, whereas forcesium it is about 125 fiK.

Other two-level cooling mechanisms using stimulatedemission processes in an intense laser standing wave havebeen proposed4 and demonstrated,5 but they will not beconsidered here. They give rise to larger friction coeffi-cients but higher equilibrium temperatures.

Three-dimensional cooling of untrapped atoms re-quires multiple laser beams. Hansch and Schawlow1

suggested a configuration of six beams arranged as three

2 0 2

NORMALIZED VELOCITY 2/^/r

Principle of Doppler cooling, (a) An atommoves along the standing wave set up by twocounterpropagating laser beams, each with afrequency below the atom's resonancefrequency by a small amount <5. (b) At lowintensities the atom feels average forces inopposite directions from the two beams (lightblue curves), with the peaks offset because ofthe laser detuning. The net force (dark bluecurve) is the friction that cools the atom. Theslope at v = o is the friction coefficient. Forthe curve shown 8 is exactly half the naturallinewidth of the excited state. Figure 1

orthogonal pairs. With the beams configured in this waythe strong damping provided by Doppler cooling canproduce not only low temperatures, but also viscousconfinement. Sodium atoms subject to the friction forcedescribed above would have such a short mean free paththat they would take longer than 1 second to diffuse acentimeter. By contrast, if they moved ballistically attheir cooling limit velocity, they would move a centimeterin 20 msec. This confinement is similar to that of aparticle in Brownian motion in a viscous fluid. Theconfinement capability of laser cooling was first realizedand demonstrated at Bell Laboratories in 1985 by StevenChu (now at Stanford University) and his colleagues.6

They gave the name "optical molasses" to this laserconfiguration. Figure 2 shows sodium atoms viscouslyconfined in an optical molasses.

The Bell Labs group measured the temperature of thesodium atoms in the "molasses" by studying their ballisticmotion after the confining laser beams were shut off. Therate at which the released atoms left the confinementvolume allowed the group to determine the temperature.The interpretation of the data depends on the dimensionsof the confinement volume and the distribution of atomswithin that volume at the time of release. The result of240 ! ;;"" //K included the expected Doppler cooling limit.Furthermore, the diffusion time of the atoms out of themolasses agreed fairly well with the expected value, sooptical molasses and the laser cooling process appeared tobe well understood.

Subsequent experiments at the National Institute ofStandards and Technology7 and at Bell Labs8 soon cast

3 4 PHYSICS TODAY OCTOBER 1990

Sodium atoms in opticalmolasses. The molasses, orregion in which the laserpressure cools and viscouslyconfines atoms, is the brightregion at the intersection ofthree orthogonal pairs ofcounterpropagating laserbeams. (Photo courtesy ofNIST.) Figure 2

doubt on the depth of this understanding. In particularthe group at NIST found that the confinement time of themolasses was optimized when the laser beams weredetuned much further from resonance than predicted bythe theory. Furthermore, the molasses was degraded bymagnetic fields too small to produce Zeeman shiftssignificant compared with either the detuning or thenatural linewidth. These and other disquieting resultsprompted the NIST team to make more precise measure-ments of the temperature. They adopted another form ofthe ballistic technique, measuring the time atoms releasedfrom the molasses took to reach a nearby probe region.Thus this time-of-flight method avoided some of the largeuncertainties of the earlier technique. The deducedvelocity spectrum does not depend as strongly on thedetails of the original confinement volume. In early 1988the new technique gave the startling result9 that thetemperature was only 40 /̂ K, much lower than thepredicted lower limit of 240 /xK. Furthermore, the lowesttemperatures were reached with the laser tuned severallinewidths from resonance, whereas the theory predictedthat the lowest temperature would occur just half alinewidth from resonance.

Such disagreements were at first difficult to believe,especially considering the attractive simplicity of theDoppler cooling theory (and the generally held belief thatexperiments never work better than one expects). Never-theless, remeasurements made by the NIST group, using avariety of techniques, and confirming experiments atStanford10 and at the Ecole Normale Superieure inParis,1' left little doubt that the Doppler cooling limit hadbeen broken. Furthermore, subsequent experiments12

showed that the low temperature was not an effect of highintensity. The temperature decreased as the intensitydecreased, indicating that the low temperatures occurredin the low-intensity regime where the Doppler coolingtheory was expected to work best. This turn of events wasboth welcome and unsettling. How were these results tobe understood?

Optical pumping induces new mechanismsThe explanation for the very low temperatures came inmid-1988, when groups at Ecole Normale Superieure1' and

at Stanford13 independently proposed new cooling mecha-nisms. These mechanisms rely upon optical pumping,light shifts and laser polarization gradients. Since then,more quantitative theories have been worked out.1415 Wewill focus here on the key ideas.

The first essential point is that alkali atoms are notsimple two-level systems. They have several Zeemansublevels in the ground state g, which are degenerate inthe absence of external fields; they correspond to thedifferent possible eigenvalues of the projection of the totalangular momentum on a given axis. These sublevels openthe door for such important physical effects as opticalpumping, which transfers atoms from one sublevel gn, of gto another gm through absorption-spontaneous emissioncycles. Such cycles occur with a mean rate P', which atlow laser intensity /, is proportional to IL and which canbe written as P' — l/r,,, where rp represents an opticalpumping time between Zeeman sublevels. As a result ofoptical pumping, a particular distribution of populations(and coherences) is reached in steady state among thevarious sublevels gm. This distribution depends on thelaser polarization.

The optical interaction also induces energy shifts fiL'in g, which are called "light shifts."16 One way ofunderstanding the light shifts is to consider the "dressed"states of the atom-laser field system. Such dressed stateshave a splitting |<5| between the atomic ground level with agiven number of photons and the excited level with onephoton less. The atom-field interaction couples these twostates of the atom-laser system with a coupling strengthcharacterized by the Rabi frequency ft. The interactioncauses the two dressed states to repel each other and, forlarge |<5|, increases the distance between them by fl2/2|<5|.The magnitude of the light shift of the atomic ground levelis half of that amount. The Rabi frequency is proportionalto the field amplitude, so that the light shifts, like thepumping rate l/rp, are proportional to I, at low /, . Theyalso depend on the laser polarization, and they vary ingeneral from one Zeeman sublevel to the other.

Another important ingredient of the new coolingmechanisms is the existence of polarization gradients,which are unavoidable in three-dimensional molasses.Because of the interference between the multiple laser

PHYSICS TODAY OCTOBER 1990 05

Light shifts in a polarizationgradient, (a) Counterpropagating

laser beams with orthogonallinear polarizations produce atotal field whose polarization

changes every eighth of awavelength from linearly

polarized to circularly polarized,as shown. An atom with no

velocity is put into such a field.The inset shows the energy levelsof the atom used in this example.

The numbers along the linesjoining the various ground andexcited-state sublevels indicate

the relative transitionprobabilities, (b) The light-

shifted energies and thepopulations of the two ground-

state sublevels of this atom. Theenergies and populations vary

with polarization and thus changewith the atom's position. The

populations are proportional tosize of solid circles. Figure 3

9 - 1/2

v* \f \ V»/

/i/4 A/2

Linear

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15

Linear Linear

9-1/2

beams, the laser polarization varies rapidly over adistance of one optical wavelength. Thus both theequilibrium population distribution among the sublevelsgm and the light shift of each sublevel depend on theposition of the atom in the laser wave.

Consider a specific simple example of the new coolingmechanisms, using a one-dimensional molasses in whichthe two counterpropagating waves have equal amplitudesand orthogonal linear polarizations. Such a laser configu-ration gives rise to strong polarization gradients becausethe polarization of the total fields changes continuouslyover one eighth of a wavelength from linear to a+

(circularly polarized in a counterclockwise direction asseen from + z axis), from a¥ to linear in the next/I/8, fromlinear to a~ (clockwise) in the next A/8 and so on as onemoves along the z axis of the stationary wave (see figure3a). In order to have at least two Zeeman sublevels in theatomic ground state g, we take the simple case of an atomictransition from the ground state with total angularmomentum Jg = '/> to the excited state e with Jr = '%.(See the inset in figure 3.)

Because of the polarization gradients, the populationsand the energies of the two ground state sublevels dependstrongly on the position of the atom along the z axis.Consider, for example, an atom at rest located at z = A/8,the polarization there being a~ (see figure 3b). Theabsorption of a a" photon can take the atom from g + 1/2 toe 1/2,from which state it can decay tog_ 1/2. (If the atomdecays tog 4 l/2 it can absorb another a~ photon and haveanother chance to arrive atg_1/2.) By contrast absorbinga <J~ photon from g . 1/2 brings the atom to e ,/2, fromwhich it can only decay to g 1/2. It follows that, in thesteady state, all of the atomic population is optically

pumped into g . 1/2. (We are assuming that the laserintensity is low enough that the excited state population isnegligible.) As shown in the inset in figure 3, the o~transition beginning ong_] / 2 is three times as intense asthe o~ transition starting from g + 1/2. Consequently thelight shift A' _ of g _1/2 is three times larger (in magnitude)than the light shift A' , of g + U2. (We assume here thatthe laser is detuned to the red, so that both light shifts arenegative.) If the atom is at z = 3/1/8, where the polariza-tion is a+, the previous conclusions are reversed. All thepopulation is in g"+1/2 and we have now A't = 3A'_ .Finally, if the atom is in a place where the polarization islinear, for example in z = 0, A/4, A/2,. . . , symmetryconsiderations show that the two sublevels are equallypopulated and undergo the same light shift. All theseresults are summarized in figure 3b, which represents as afunction of 2 the light-shifted energies and the populationsof the two ground state sublevels for an atom at rest in z.

Clearly the force on an atom at rest spatially averagesto zero, because the population is symmetrically distribut-ed around the hills and the valleys. If the atom moves, thesymmetry is disturbed, and an average friction forceappears. The key point is that optical pumping, whichestablishes the population distribution, takes a finite timeTV. Consider, for example, an atom moving to the rightand starting at 2 = A/8, where the population is pumpedinto the bottom of the valley (see figure 4). If the velocity vis such that the atom travels over a distance of the order ofi /4 during rp, the atom will on the average remain on thesame sublevel and climb up the potential hill. At the topof the hill, it has the highest probability of being opticallypumped to the bottom of the potential valley. From there,the same sequence can be repeated, as indicated by the

36 PHYSICS TODAY OCTOBER 1990

solid curves in figure 4. Because of the time lag rp, theatom, like Sisyphus in Greek mythology, always seems tobe climbing potential hills, transforming part of its kineticenergy into potential energy.

The previous physical picture clearly shows that thisnew cooling mechanism is most effective when the atomtravels a distance of the order of A during the opticalpumping time rp. Thus the velocity-capture range isdenned by vp ~A/TP , or equivalently kvp ~ l/rp. Becausethe optical pumping rate is proportional to the laserintensity 7L, the range vp is also proportional to 7L andtends to zero as /[, goes to zero. This contrasts with thecase for Doppler cooling, where the velocity-capture rangeuD is independent of IL. On the other hand the friction co-efficient a of the new cooling mechanism remains largeand independent of IL, whereas it was proportional to 7L inDoppler cooling. This important (and rather counterintui-tive) property results because when IL tends to zero, thelong optical pumping times compensate for the weaknessof the light shifts.

While the friction coefficient a does not depend on thelaser intensity, the heating rate does. The temperature towhich the atoms are cooled depends on the ratio of theheating rate to the friction coefficient, so the temperatureis proportional to IL. The friction and heating also dependon the laser detuning in such a way that at large detuningthe temperature is inversely proportional to 8.

Figure 5 compares in a qualitative way the behavior ofDoppler and polarization gradient cooling forces fordifferent intensities. Clearly the Doppler force maintainsthe same capture range for increasing intensity while thefriction coefficient (the slope at v = 0) increases. Inpolarization gradient cooling, on the other hand, it is thefriction coefficient that remains constant (and quite large)and the capture range (which may be quite small) thatincreases. At low velocity, polarization gradient cooling is

generally the more effective mechanism. For highervelocities, depending on the laser parameters, the Dopplercooling may be better.

Other laser configurations can produce cooling exhi-biting the same properties. Some of these have polariza-tion gradients without any Sisyphus effect. (See, forexample the a+-a~ configurations studied in references14 and 15.) Others use a Sisyphus effect appearing in astanding wave having no polarization gradient but subject-ed to a weak static magnetic field.171H All these newcooling mechanisms, as well as the one described above,share the following features: When the multilevel atom isat rest at a position z the density matrix <rsl(z), whichdescribes the steady-state distribution of populations (andcoherences) in the ground state, strongly depends on z, ona wavelength scale. Because optical pumping takes afinite time rp, when the atom is moving, its internal statea (z) cannot follow adiabatically the variations of the laserfield due to atomic motion: a (z) lags behind asi (z) with adelay of the order of rp. It is precisely this time lag rp thatis responsible for the new friction mechanism. The timelag becomes longer when the laser intensity becomessmaller, and the friction mechanism retains its effective-ness even as the intensity is lowered.

Comparing experiment and theoryThis theory of a new laser cooling force caused by spatiallydependent optical pumping, although formulated only inone-dimension, accounted for most of the major featuresobserved in three-dimensional optical molasses. Theextremely low temperatures, as well as the dependence ofthe temperature on laser intensity and on detuning, wereall consistent with the predictions of the new theory.Furthermore, the extreme sensitivity of the molasses tothe magnetic field could be understood on the grounds thatthe magnetic field shifts and mixes the Zeeman sublevels,

A/4 A/2ATOMIC POSITION

Forever climbing hills, as did Sisyphusin the Creek myth, an atom that istraveling in the laser configuration offigure 3 moves away from a potentialvalley and reaches a potential hillbefore being optically pumped to thebottom of another valley. On theaverage, the atom sees more uphill partsthan downhill ones, and the net energyloss cools it. The effect is nearmaximum in the special case shownhere because the atom travels onefourth of a wavelength in the mean time7"p that an atom waits beforeundergoing an optical pumping cycle.Figure 4

PHYSICS TODAY OCTOBER 1990 3 7

60

0.5

INTENSITY/DETUNING lL/6

Temperature depends linearly on I, 18, whereIL is the laser intensity and S is the laser detun-ing. These experimental results agree with thetheory for polarization-gradient cooling. Sym-bols corresponds to different values of detuning.(Adapted from ref. 20.) Figure 6

Damping force in Doppler cooling (a) and inpolarization-gradient cooling (b). Horizontal axes arethe normalized velocities 2kvlV, where k is thewavevector of the laser beams and F is the linewidth ofthe atomic resonance. Curves are shown for anarbitrary intensity I,, (dark) and for l o /2 (mediumshade) and l0 /4 (light). For Doppler cooling, thevelocity range over which cooling remains effective isindependent of intensity while the friction coefficient(slope of the force curve at v = 0) increases withincreasing intensities. By contrast, for polarizationcooling the velocity range increases for increasingintensities while the friction coefficient stays constantand large. Note the different horizontal scales. Figure 5

frustrating the cooling mechanism that depends on opticalpumping and light shifts of these same levels. The newtheory also led to a testable prediction: The magnetic fieldshould inhibit the cooling less at higher laser intensitybecause the field competes with larger light shifts andoptical pumping rates. The confirmation19 of this newprediction indicated that the theory was at least qualita-tively correct. Another positive indication was the obser-vation at Stanford17 of nonthermal, bimodal velocitydistributions, indicating a velocity-capture range smallerthan for Doppler cooling. Because the velocity-capturerange of the cooling force is proportional to the laserintensity, there will be a nonzero threshold laser intensityfor which the cooling works, in contrast to the case forDoppler cooling. The team at NIST qualitatively con-firmed the existence of such a threshold.19

Although the new cooling mechanism was first foundin sodium, this atom has not proved to be an ideal testingground for the theory. The particular hyperfine spectro-scopic structure of sodium prevents the molasses fromworking as the laser is detuned far from resonance. Thislarge detuning limit is exactly where the theory issimplest and least dependent on the details of thepolarization gradients. Experiments at the Ecole Nor-male Superieure using cesium, which has a much largerhyperfine structure, have been able to explore the largedetuning limit and show striking agreement between theone-dimension theory and the three-dimensional experi-ments.20 The theory predicts that the temperature islinearly dependent on the ratio of laser intensity todetuning. Figure 6 shows the temperature for atoms in acesium molasses for a wide range of detunings andintensities. All except the smallest detunings and highestintensities follow the expected dependences. The lowerlimit to the intensity for which the cooling works followsthe expected dependence on detuning.

The lowest temperature obtained in these experi-ments on cesium is 2.5 + 0.6 fiK, representing the coldestkinetic temperature yet reported for any sample of atomsin a three-dimensional cooling arrangement. Figure 7shows a typical experimental time-of-flight spectrum fromwhich this temperature is deduced. Carl Wieman and hiscolleagues at the Joint Institute for Laboratory Astrophys-ics have recently observed21 similarly low temperatures.This temperature for cesium and the 25-fiK temperaturesfor sodium measured in a three-dimensional configurationby the NIST19 and Stanford17 groups represent rmsvelocities just a few times the velocity of recoil fromabsorption or emission of a single photon.

Below the recoil energyIn all the previous cooling schemes, the cooled atomsconstantly absorb and reemit light, so that it seems

3 8 PHYSICS TODAY OCTOBER 1990

impossible to avoid the random recoil due to spontaneous-ly emitted photons. The fundamental limit for lasercooling is therefore expected to be on the order ofEm = fi2k2/2M, where M is the atomic mass. Actually,this limit does not always hold: At least in one-dimension,the recoil limit can be overcome with a completelydifferent cooling mechanism that was demonstrated in1988 by the group at the Ecole Normale Superieure.22

This new mechanism is based on "velocity-selectivecoherent population trapping." Coherent population trap-ping means that atoms are prepared in a coherentsuperposition of two ground state sublevels that cannotabsorb light; the two absorption amplitudes starting fromthese two sublevels have completely destructive interfer-ence with each other. Once the atoms are opticallypumped into such a trapping state, the fluorescence stops.This well-known phenomenon was observed"' for the firsttime at the University of Pisa in 1976. The team at theEcole Normale Superieure in 1988 introduced the newtrick of making the trapping state velocity selective andtherefore usable for laser cooling. They accomplished thiswith a one-dimensional molasses where the two counter-propagating laser beams had opposite circular polariza-tions. One can show that the trapping state exists only foratoms with zero velocity.2224 If u^O, the interferencebetween the two transition amplitudes starting from thetwo ground state sublevels is no longer completelydestructive and the atom can absorb light. The larger v is,the higher the absorption rate. The challenge of course isto populate the nonabsorping trapping state.

The idea is to use the atomic momentum redistribu-tion that accompanies an absorption-spontaneous emis-sion cycle: There is a certain probability for an atominitially in an absorbing velocity class (vj^O) to be opticallypumped into the v = 0 nonabsorbing trapping state.When this happens, the atoms are "hidden" from the lightand so protected from the random recoils. Thus theyremain at v = 0. Atoms should therefore pile up in anarrow velocity interval Su around v = 0. Atoms for whichv is not exactly 0 are not perfectly trapped: As a result thewidth Sv of the interval around v = 0 is determined by theinteraction time ©. For a given 0 the only atoms that canremain trapped are those for which the absorption ratetimes 0 is smaller than 1. Since the absorption rateincreases with v, the larger 0, the smaller v for theremaining atoms. There is no lower limit to the velocitywidth that can be reached by such a method, provided ofcourse that the interaction time can be made long enough.This kind of cooling differs from all the previous coolingmechanisms in that friction is not involved. Instead, thecold atoms are selected by a combination of opticalpumping and filtering processes that accumulate them ina small domain in one-dimensional velocity space.

g 0.5CD

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100 120TIME OF FLIGHT (msec)

140

Time of flight distribution for cesium atomsthat were released from an optical molasses andtraveled 7 cm from there to a probe. The curveimplies a temperature of 2.5 ju,K, a record lowtemperature. (Adapted from ref. 20.) Figure 7

The discussion so far has been oversimplified. A morecareful analysis,2224 using a quantum description of theatomic translational degrees of freedom along the direc-tion z of the two counterpropagating laser waves, showsthat the trapping state is a linear combination of twoatomic states differing not only by the internal Zeemanquantum number but also by the momentum quantumnumber p along z. The trapping state is therefore a doublemomentum state. Indeed, the experimental results ob-tained at Ecole Normale Superieure for the momentumdistribution along z of helium-4 atoms cooled by thismethod22 exhibit a double-peak structure (see figure 8), aspredicted theoretically. The width of each peak is smallerthan the photon momentum, fik, which verifies thatvelocity widths have gone below the recoil limit. The one-dimensional temperature (determined by the componentof velocity along the laser axis) corresponding to theseobserved widths is of the order of 2 /iK. Possible two-dimensional extensions,24-25 as well as three-dimensionalextensions2526 of this cooling scheme have been recentlyproposed, leading to trapping states that are linearcombinations of several momentum eigenstates whosemomenta point in different directions, but all have themagnitude fik.

A combination of known effectsIn conclusion we would like to stress that the new physicalmechanisms that have made it possible to cool atoms to themicrokelvin range are based on physical effects, such asoptical pumping, light shifts and coherent populationtrapping, that have been known for a long time. Forexample, the first observation of light shifts27 predates theuse of lasers for atomic spectroscopy: Kastler called them"lamp shifts" in a word play indicating that they wereproduced by light from a lamp. The researchers of 30years ago fully realized that the differential light shifts ofthe ground state Zeeman sublevels depended strongly onthe polarization of the light. The use of optical pumping to

PHYSICS TODAY OCTOBER 1990 3 9

MOMENTUM

Distribution of atomic momenta in thedirection of the laser beam for helium-4 atomscooled by the velocity-selective coherent-population trapping method (red). The widthof each peak is less than the momentum ftk ofa single photon, indicating cooling below therecoil limit. The uncooled atomic momentumdistribution is shown in black. (Adapted fromref. 22.) Figure 8

differentially populate Zeeman sublevels is even older.For us it has been especially appealing to see such well-known physical effects acquire new life as they conspire inquite unexpected ways to cool atoms to the lowest kinetictemperatures ever measured.

The authors wish to thank La Direction des Recherches, Etudes etTechniques, the European Economic Community and the USOffice of Naval Research for support of activities in their respectivelaboratories.

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