In June 1995 our research group atthe Joint Institute for LaboratoryAstrophysics (now called JILA) in

Boulder, Colo., succeeded in creating aminuscule but marvelous droplet. Bycooling 2,000 rubidium atoms to atemperature less than 100 billionths ofa degree above absolute zero (100 bil-lionths of a degree kelvin), we causedthe atoms to lose for a full 10 secondstheir individual identities and behave asthough they were a single “superatom.”The atoms’ physical properties, such astheir motions, became identical to oneanother. This Bose-Einstein condensate(BEC), the first observed in a gas, canbe thought of as the matter counterpartof the laser—except that in the conden-sate it is atoms, rather than photons,that dance in perfect unison.

Our short-lived, gelid sample was theexperimental realization of a theoreticalconstruct that has intrigued scientistsever since it was predicted some 73 yearsago by the work of physicists Albert Ein-stein and Satyendra Nath Bose. At ordi-nary temperatures, the atoms of a gasare scattered throughout the containerholding them. Some have high energies(high speeds); others have low ones. Ex-panding on Bose’s work, Einsteinshowed that if a sample of atoms werecooled sufficiently, a large fraction ofthem would settle into the single lowestpossible energy state in the container. Inmathematical terms, their individualwave equations—which describe suchphysical characteristics of an atom asits position and velocity—would in ef-fect merge, and each atom would be-come indistinguishable from any other.

Progress in creating Bose-Einstein con-densates has sparked great interest in thephysics community and has even gener-ated coverage in the mainstream press.At first, some of the attention derivedfrom the drama inherent in the decades-

long quest to prove Einstein’s theory. Butmost of the fascination now stems fromthe fact that the condensate offers amacroscopic window into the strangeworld of quantum mechanics, the theoryof matter based on the observation thatelementary particles, such as electrons,have wave properties. Quantum me-chanics, which encompasses the famousHeisenberg uncertainty principle, usesthese wavelike properties to describethe structure and interactions of matter.

We can rarely observe the effects ofquantum mechanics in the behavior ofa macroscopic amount of material. Inordinary, so-called bulk matter, the in-coherent contributions of the uncount-ably large number of constituent parti-cles obscure the wave nature of quan-tum mechanics, and we can only infer itseffects. But in Bose condensation, thewave nature of each atom is precisely inphase with that of every other. Quan-tum-mechanical waves extend acrossthe sample of condensate and can beobserved with the naked eye. The sub-microscopic thus becomes macroscopic.

New Light on Old Paradoxes

The creation of Bose-Einstein con-densates has cast new light on long-

standing paradoxes of quantum me-chanics. For example, if two or moreatoms are in a single quantum-mechan-ical state, as they are in a condensate, itis fundamentally impossible to distin-guish them by any measurement. Thetwo atoms occupy the same volume ofspace, move at the identical speed, scat-ter light of the same color and so on.

Nothing in our experience, based asit is on familiarity with matter at nor-mal temperatures, helps us comprehendthis paradox. That is because at normaltemperatures and at the size scales weare all familiar with, it is possible to de-

The Bose-Einstein Condensate40 Scientific American March 1998

The Bose-Einstein CondensateThree years ago in a Colorado laboratory, scientists

realized a long-standing dream, bringing the quantum world closer to the one of everyday experience

by Eric A. Cornell and Carl E. Wieman

ATOMIC TRAP cools by means of twodifferent mechanisms. First, six laserbeams (red) cool atoms, initially at roomtemperature, while corralling them towardthe center of an evacuated glass box. Next,the laser beams are turned off, and themagnetic coils (copper) are energized. Cur-rent flowing through the coils generates amagnetic field that further confines mostof the atoms while allowing the energeticones to escape. Thus, the average energyof the remaining atoms decreases, makingthe sample colder and even more closelyconfined to the center of the trap. Ulti-mately, many of the atoms attain the low-est possible energy state allowed by quan-tum mechanics and become a single entityknown as a Bose-Einstein condensate.

Copyright 1998 Scientific American, Inc.

scribe the position and motion of eachand every object in a collection of ob-jects. The numbered Ping-Pong ballsbouncing in a rotating drum used to se-lect lottery numbers exemplify the mo-tions describable by classical mechanics.

At extremely low temperatures or atsmall size scales, on the other hand, theusefulness of classical mechanics beginsto wane. The crisp analogy of atoms asPing-Pong balls begins to blur. We can-not know the exact position of eachatom, which is better thought of as ablurry spot. This spot—known as a wavepacket—is the region of space in which

we can expect to find the atom. As acollection of atoms becomes colder, thesize of each wave packet grows. As longas each wave packet is spatially sepa-rated from the others, it is possible, atleast in principle, to tell atoms apart.When the temperature becomes suffi-ciently low, however, each atom’s wavepacket begins to overlap with those ofneighboring atoms. When this happens,the atoms “Bose-condense” into thelowest possible energy state, and thewave packets coalesce into a single, mac-roscopic packet. The atoms undergo aquantum identity crisis: we can no long-

er distinguish one atom from another.The current excitement over these

condensates contrasts sharply with thereaction to Einstein’s discovery in 1925that they could exist. Perhaps becauseof the impossibility then of reaching therequired temperatures—less than a mil-lionth of a degree kelvin—the hypothe-sized gaseous condensate was consid-ered a curiosity of questionable validityand little physical significance. For per-spective, even the coldest depths of in-tergalactic space are millions of timestoo hot for Bose condensation.

In the intervening decades, however,

The Bose-Einstein Condensate Scientific American March 1998 41

MIC

HA

EL G

OO

DM

AN

Copyright 1998 Scientific American, Inc.

Bose condensation came back into fash-ion. Physicists realized that the conceptcould explain superfluidity in liquid he-lium, which occurs at much higher tem-peratures than gaseous Bose condensa-tion. Below 2.2 kelvins, the viscosity ofliquid helium completely disappears—

putting the “super” in superfluidity.Not until the late 1970s did refrigera-

tion technology advance to the pointthat physicists could entertain the no-tion of creating something like Einstein’soriginal concept of a BEC in a gas. Lab-oratory workers at M.I.T., the Universityof Amsterdam, the University of BritishColumbia and Cornell University hadto confront a fundamental difficulty. Toachieve such a BEC, they had to coolthe gas to far below the temperature atwhich the atoms would normally freezeinto a solid. In other words, they had tocreate a supersaturated gas. Their ex-pectation was that hydrogen would su-persaturate, because the gas was knownto resist the atom-by-atom clumpingthat precedes bulk freezing.

Although these investigators have notyet succeeded in creating a Bose-Ein-stein condensate with hydrogen, theydid develop a much better understand-ing of the difficulties and found cleverapproaches for attacking them, whichbenefited us. In 1989, inspired by thehydrogen work and encouraged by ourown research on the use of lasers to trapand cool alkali atoms, we began to sus-pect that these atoms, which include ce-sium, rubidium and sodium, wouldmake much better candidates than hy-drogen for producing a Bose conden-sate. Although the clumping propertiesof cesium, rubidium and sodium are notsuperior to those of hydrogen, the rateat which those atoms transform them-selves into condensate is much faster

than the rate for hydrogen atoms. Thesemuch larger atoms bounce off one an-other at much higher rates, sharing en-ergy among themselves more quickly,which allows the condensate to formbefore clumping can occur.

Also, it looked as if it might be rela-tively easy and inexpensive to get theseatoms very cold by combining ingenioustechniques developed for laser coolingand trapping of alkali atoms with thetechniques for magnetic trapping andevaporative cooling developed by the re-searchers working with hydrogen. Theseideas were developed in a series of dis-cussions with our friend and formerteacher, Daniel Kleppner, the co-leaderof a group at M.I.T. that is attemptingto create a condensate with hydrogen.

Our hypothesis about alkali atomswas ultimately fruitful. Just a fewmonths after we succeeded with rubidi-um, Wolfgang Ketterle’s group at M.I.T.produced a Bose condensate with sodi-um atoms; since that time, Ketterle’steam has succeeded in creating a con-densate with 10 million atoms. At thetime of this writing, there are at leastseven teams producing condensates.Besides our own group, others workingwith rubidium are Daniel J. Heinzen ofthe University of Texas at Austin, Ger-hard Rempe of the University of Kon-stanz in Germany and Mark Kasevichof Yale University. In sodium, besidesKetterle’s at M.I.T., there is a group ledby Lene Vestergaard Hau of the Row-land Institute for Science in Cambridge,

MIC

HA

EL G

OO

DM

AN

EVAPORATIVE COOLING occurs in a magnetic trap, which can be thought of as adeep bowl (blue). The most energetic atoms, depicted with the longest green trajectoryarrows, escape from the bowl (above, left). Those that remain collide with one anotherfrequently, apportioning out the remaining energy (left). Eventually, the atoms move soslowly and are so closely packed at the bottom of the bowl that their quantum naturebecomes more pronounced. So-called wave packets, representing the region where eachatom is likely to be found, become less distinct and begin to overlap (below, left). Ulti-mately, two atoms collide, and one is left as close to stationary as is allowed by Heisen-berg’s uncertainty principle. This event triggers an avalanche of atoms piling up in thelowest energy state of the trap, merging into the single ground-state blob that is a Bose-Einstein condensate (below, center and right).

Copyright 1998 Scientific American, Inc.

Mass. At Rice University Randall G.Hulet has succeeded in creating a con-densate with lithium.

All these teams are using the samebasic apparatus. As with any kind ofrefrigeration, the chilling of atoms re-quires a method of removing heat andalso of insulating the chilled samplefrom its surroundings. Both functionsare accomplished in each of two steps.In the first, the force of laser light on theatoms both cools and insulates them. Inthe second, we use magnetic fields to in-sulate, and we cool by evaporation.

Laser Cooling and Trapping

The heart of our apparatus is a smallglass box with some coils of wire

around it [see illustration on pages 40and 41]. We completely evacuate thecell, producing in effect a superefficientthermos bottle. Next, we let in a tinyamount of rubidium gas. Six beams oflaser light intersect in the middle of thebox, converging on the gas. The laserlight need not be intense, so we obtainit from inexpensive diode lasers, similarto those found in compact-disc players.

We adjust the frequency of the laserradiation so that the atoms absorb itand then reradiate photons. An atomcan absorb and reradiate many millionsof photons each second, and with eachone, the atom receives a minuscule kickin the direction the absorbed photon ismoving. These kicks are called radiationpressure. The trick to laser cooling is toget the atom to absorb mainly photonsthat are traveling in the direction oppo-site that of the atom’s motion, therebyslowing the atom down (cooling it, inother words). We accomplish this featby carefully adjusting the frequency of

the laser light relative to the frequencyof the light absorbed by the atoms [seeillustration above].

In this setup, we use laser light notonly to cool the atoms but also to “trap”them, keeping them away from theroom-temperature walls of the cell. Infact, the two laser applications are sim-ilar. With trapping, we use the radiationpressure to oppose the tendency of theatoms to drift away from the center ofthe cell. A weak magnetic field tunes theresonance of the atom to absorb prefer-entially from the laser beam that ispointing toward the center of the cell(recall that six laser beams intersect atthe center of the cell). The net effect isthat all the atoms are pushed towardone spot and are held there just by theforce of the laser light.

These techniques fill our laser trap inone minute with 10 million atoms cap-tured from the room-temperature ru-bidium vapor in the cell. These trappedatoms are at a temperature of about 40millionths of a degree above absolutezero—an extraordinarily low tempera-ture by most standards but still 100times too hot to form a BEC. In the pres-ence of the laser light, the unavoidablerandom jostling the atoms receive fromthe impact of individual light photonskeeps the atoms from getting any cold-er or denser.

To get around the limitations imposedby those random photon impacts, weturn off the lasers at this point and acti-vate the second stage of the cooling pro-cess. This stage is based on the magnet-ic-trapping and evaporative-coolingtechnology developed in the quest toachieve a condensate with hydrogenatoms. A magnetic trap exploits the factthat each atom acts like a tiny bar mag-

net and thus is subjected to a force whenplaced in a magnetic field [see illustra-tion on opposite page]. By carefully con-trolling the shape of the magnetic fieldand making it relatively strong, we canuse the field to hold the atoms, whichmove around inside the field much likeballs rolling about inside a deep bowl.In evaporative cooling, the most ener-getic atoms escape from this magneticbowl. When they do, they carry awaymore than their share of the energy,leaving the remaining atoms colder.

The analogy here is to cooling coffee.The most energetic water molecules leapout of the cup into the room (as steam),thereby reducing the average energy ofthe liquid that is left in the cup. Mean-while countless collisions among the re-maining molecules in the cup apportionout the remaining energy among allthose molecules. Our cloud of magneti-cally trapped atoms is at a much lowerdensity than water molecules in a cup.So the primary experimental challengewe faced for five years was how to getthe atoms to collide with one anotherenough times to share the energy beforethey were knocked out of the trap by acollision with one of the untrapped,room-temperature atoms remaining inour glass cell.

Many small improvements, ratherthan a single breakthrough, solved thisproblem. For instance, before assem-bling the cell and its connected vacuumpump, we took extreme care in cleaningeach part, because any remaining resi-dues from our hands on an inside sur-face would emit vapors that would de-grade the vacuum. Also, we made surethat the tiny amount of rubidium vaporremaining in the cell was as small as itcould be while providing a sufficientnumber of atoms to fill the optical trap.

Incremental steps such as these helpedbut still left us well shy of the densityneeded to get the evaporative coolingunder way. The basic problem was theeffectiveness of the magnetic trap. Al-though the magnetic fields that make

The Bose-Einstein Condensate Scientific American March 1998 43

LASER COOLING of an atom makes useof the pressure, or force, exerted by re-peated photon impacts. An atom movingagainst a laser beam encounters a higherfrequency than an atom moving with thesame beam. In cooling, the frequency ofthe beam is adjusted so that an atommoving into the beam scatters many morephotons than an atom moving away fromthe beam. The net effect is to reduce thespeed and thus cool the atom.

FORCE

FORCE

VELOCITY

VELOCITY

MIC

HA

EL G

OO

DM

AN

Copyright 1998 Scientific American, Inc.

up the confining magnetic “bowl” canbe quite strong, the little “bar magnet”inside each individual atom is weak.This characteristic makes it difficult topush the atom around with a magneticfield, even if the atom is moving quiteslowly (as are our laser-cooled atoms).

In 1994 we finally confronted the needto build a magnetic trap with a narrow-er, deeper bowl. Our quickly built, nar-row-and-deep magnetic trap proved tobe the final piece needed to cool evap-oratively the rubidium atoms into acondensate. As it turns out, our partic-ular trap design was hardly a uniquesolution. Currently there are almost asmany different magnetic trap configu-rations as there are groups studyingthese condensates.

Shadow Snapshot of a “Superatom”

How do we know that we have infact produced a Bose-Einstein con-

densate? To observe the cloud of cooledatoms, we take a so-called shadow snap-shot with a flash of laser light. Becausethe atoms sink to the bottom of the mag-netic bowl as they cool, the cold cloud istoo small to see easily. To make it larg-er, we turn off the confining magneticfields, allowing the atoms to fly out free-ly in all directions. After about 0.1 sec-ond, we illuminate the now expandedcloud with a flash of laser light. The

atoms scatter this light out of the beam,casting a shadow that we observe witha video camera. From this shadow, wecan determine the distribution of veloc-ities of the atoms in the original trappedcloud. The velocity measurement alsogives us the temperature of the sample.

In the plot of the velocity distribution[see illustration on opposite page], thecondensate appears as a dorsal-fin-shaped peak. The condensate atomshave the smallest possible velocity andthus remain in a dense cluster in thecenter of the cloud after it has expand-ed. This photograph of a condensate isfurther proof that there is somethingwrong with classical mechanics. Thecondensate forms with the lowest pos-sible energy. In classical mechanics,“lowest energy” means that the atomsshould be at the center of the trap andmotionless, which would appear as aninfinitely narrow and tall peak in our im-age. The peak differs from this classicalconception because of quantum effectsthat can be summed up in three words:Heisenberg’s uncertainty principle.

The uncertainty principle puts limitson what is knowable about anything,including atoms. The more preciselyyou know an atom’s location, the lesswell you can know its velocity, and viceversa. That is why the condensate peakis not infinitely narrow. If it were, wewould know that the atoms were in the

exact center of the trap and had exactlyzero energy. According to the uncer-tainty principle, we cannot know boththese things simultaneously.

Einstein’s theory requires that theatoms in a condensate have energy thatis as low as possible, whereas Heisen-berg’s uncertainty principle forbids themfrom being at the very bottom of thetrap. Quantum mechanics resolves thisconflict by postulating that the energyof an atom in any container, includingour trap, can only be one of a set of dis-crete, allowed values—and the lowestof these values is not quite zero. Thislowest allowed energy is called the zero-point energy, because even atoms whosetemperature is exactly zero have thisminimum energy. Atoms with this ener-gy move around slowly near—but notquite at—the center of the trap. The un-certainty principle and the other laws ofquantum mechanics are normally seenonly in the behavior of submicroscopicobjects such as a single atom or smaller.The Bose-Einstein condensate thereforeis a rare example of the uncertainty prin-ciple in action in the macroscopic world.

Bose-Einstein condensation of atomsis too new, and too different, for us tosay if its usefulness will eventually ex-tend beyond lecture demonstrations forquantum mechanics. Any discussion ofpractical applications for condensatesmust necessarily be speculative. Never-

6 5

MILLIMETERS

4 3 2 1 0

300 KELVIN

293 KELVIN:ROOMTEMPERATURE

273 KELVIN:WATER FREEZES

LOS ANGELES

SAN BERNARDINO

ARIZONA-CALIFORNIABORDER

TAOS, N.M. TERRE HAUTE, IND. RARITAN, N.J.

PLAINFIELD, N.J.

41ST STREET & 8TH AVENUENEW YORK CITY

TIMES SQUARE BUILDING42ND STREET & BROADWAYNEW YORK CITY

216 KELVIN:SOUTH POLEWINTERTIME

77 KELVIN:AIR FREEZES 4 KELVIN:

HELIUMLIQUEFIES

3 KELVIN:INTERGALACTIC

SPACE

0.02 KELVIN:LOWEST-TEMPERATUREHELIUM REFRIGERATOR

50 NANOKELVIN:APPROXIMATE

TEMPERATURE OFNEARLY PURECONDENSATE

400 NANOKELVIN: BOSE-EINSTEIN

CONDENSATEFIRST APPEARS

IN RUBIDIUM

0.5mm

0.60.683

5.4

0.7

CONTINENT-WIDE THERMOMETER is 4,100 kilometers (2,548 miles)long and shows how low the temperature must be before a condensate canform. With zero degrees kelvin in Times Square in New York City and 300 de-grees assigned to City Hall in Los Angeles, room temperature corresponds toSan Bernardino, Calif., and the temperature of air, frozen solid, to Terre Haute,Ind. The temperature of a nearly pure condensate is a mere 0.683 millimeterfrom the thermometer’s zero point.

MA

RK G

ERB

ER

The Bose-Einstein Condensate44 Scientific American March 1998 Copyright 1998 Scientific American, Inc.

theless, our musings can be guided by astriking physical analogy: the atomsthat make up a Bose condensate are inmany ways the analogue to the photonsthat make up a laser beam.

The Ultimate in Precise Control?

Every photon in a laser beam travelsin exactly the same direction and

has the same frequency and phase ofoscillation. This property makes laserlight very easy to control precisely andleads to its utility in compact-discplayers, laser printers and other ap-pliances. Similarly, Bose condensationrepresents the ultimate in precise con-trol—but for atoms rather than photons.The matter waves of a Bose condensatecan be reflected, focused, diffracted andmodulated in frequency and amplitude.This kind of control will very likely leadto improved timekeeping; the world’sbest clocks are already based on the os-cillations of laser-cooled atoms. Appli-cations may also turn up in other areas.In a flight of fancy, it is possible toimagine a beam of atoms focused to aspot only a millionth of a meter across,“airbrushing” a transistor directly ontoan integrated circuit.

But for now, many of the propertiesof the Bose-Einstein condensate remainunknown. Of particular interest is thecondensate’s viscosity. The speculationnow is that the viscosity will be vanish-ingly small, making the condensate akind of “supergas,” in which ripples andswirls, once excited, will never dampdown. Another area of curiosity centerson a basic difference between laser lightand a condensate. Laser beams are non-interacting—they can cross without af-fecting one another at all. A condensate,on the other hand, has some resistanceto compression and some springiness—

it is, in short, a fluid. A material that is

both a fluid and acoherent wave is go-ing to exhibit behav-ior that is rich, whichis a physicist’s way of saying that it isgoing to take a long time to figure out.

Meanwhile many groups have beguna variety of measurements on the con-densates. In a lovely experiment, Ketter-le’s group has already shown that whentwo separate clouds of Bose condensateoverlap, the result is a fringe pattern ofalternating constructive and destructiveinterference, just as occurs with inter-secting laser radiation. In the atom cloud,these regions appear respectively as

stripes of high density and low density.Our group has looked at how the in-teractions between the atoms distortthe shape of the atom cloud and themanner in which it quivers after wehave “poked” it gently with magneticfields. A number of other teams arenow devising their own experiments tojoin in this work.

As the results begin to accrue fromthese and other experiments over thenext several years, we will improve ourunderstanding of this singular state ofmatter. As we do, the strange, fascinat-ing quantum-mechanical world willcome a little bit closer to our own.

The Bose-Einstein Condensate Scientific American March 1998 45

The Authors

ERIC A. CORNELL and CARL E. WIEMAN are both fel-lows of JILA, the former Joint Institute for Laboratory Astro-physics, which is staffed by the National Institute of Stan-dards and Technology (NIST) and the University of Colorado.Cornell, a physicist at NIST and a professor adjoint at the uni-versity, was co-leader, with Wieman, of the team at JILA thatproduced the first Bose-Einstein condensate in a gas. Wieman,a professor of physics at the university, is also known for hisstudies of the breakdown of symmetry in the interactions ofelementary particles. The authors would like to thank theircolleagues Michael Anderson, Michael Matthews and JasonEnsher for their work on the condensate project.

Further Reading

New Mechanisms for Laser Cooling. William D. Phillips and ClaudeCohen-Tannoudji in Physics Today, Vol. 43, pages 33–40; October 1990.

Observation of Bose-Einstein Condensation in a Dilute AtomicVapor. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wiemanand E. A. Cornell in Science, Vol. 269, pages 198–201; July 14, 1995.

Bose-Einstein Condensation. Edited by A. Griffin, D. W. Snoke and S. Stringari. Cambridge University Press, 1995.

Observation of Interference between Two Bose Condensates. M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurnand W. Ketterle in Science, Vol. 275, pages 637–641; January 31, 1997.

Bose-Einstein Condensation. World Wide Web site available at http:// www.colorado.edu/physics/2000/bec

SHADOW IMAGE of a forming Bose-Einstein condensate was processed by a com-puter to show more clearly the distribution of velocities of atoms in the cold cloud. Topand bottom images show the same data but from different angles. In the upper set,where the surface appears highest corresponds to where the atoms are the most closelypacked and are barely moving. Before the condensate appears (left), the cloud, at about200 billionths of a degree kelvin, is a single, relatively smooth velocity distribution. Af-ter further cooling to 100 billionths of a degree, the conden-sate appears as a region of almost sta-tionary atoms in the center of the distri-bution (center). After still more cooling,only condensate remains (right).

JILA

SA

Copyright 1998 Scientific American, Inc.