features Physics World March 1997 29 Bose-Einstein condensation is an exotic quantum phenomenon that was observed in dilute atomic gases for the first time in 1995, and is now the subject of intense theoretical and experimental study Bose-Einstein condensation CHRISTOPHER TOWNSEND, WOLFGANG KETTERLE AND SANDRO STRINGARI IN 1924 the Indian physicist Satyendra Nath Bose sent Order reigns in the ground state Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of The dynamical behaviour of a gas at room temperature is identical particles. Einstein generalized Bose's theory to not affected by the fact that one atom cannot be distin- an ideal gas of identical atoms or molecules for which the guished from another. In accordance with the Heisenberg number of particles is conserved and, in the same year, uncertainty principle, the position of an atom is smeared predicted that at sufficiently low temperatures the par- out over a distance given by the thermal de Broglie wave- 2 12 ticles would become locked together in the lowest quan- length, XdB = (2TtH /kBmTy , where kB is the Boltzmann tum state of the system. We now know that this phenomenon, called Bose-Einstein condensation radio-frequency (BEC), only happens for "bosons" - particles antenna with a total spin that is an integer multiple of % curvature coil bias field coil the Planck constant divided by 2n. This Bose condensate, and the process of con- densation itself, was predicted to have many unusual properties and for years experimenters have tried to produce Bose-Einstein condensa- tion in the laboratory. Finally in 1995 groups at JILA, a laboratory run by the National Institute of Standards and Technology and the University of Colorado in Boulder, Colorado, and the Massachusetts Institute of Technology (MIT) obtained compelling evidence for Bose-Einstein condensation in dilute atomic gases. Both the Boulder and MIT groups, and a group at Rice University in Houston, Texas, have since improved the techniques for creating and observing this exotic quantum phenomenon, and rapid progress has been made in under- standing its dynamic and thermodynamic prop- 1 The set-up for evaporative cooling from the cloverieaf magnetic trap at MIT. The erties. At MIT we have recently verified the central (curvature) coils provide axial confinement while the outer colls (the "cloverleaves" or gradient coils) give tight radial confinement. The resulting intriguing feature that Bose-condensed atoms anisotroplc potential gives rise to cigar-shaped clouds. Radio-frequency radiation are "laser-like" - in other words, that the matter from an antenna selectively flips the spin of the most energetic atoms, and waves of the atoms are coherent. In these experi- the remaining atoms retheimalize to a lower temperature. Cooling Is forced by ments we have succeeded in observing coher- lowering the radio-frequency. ence directly, and have demonstrated a rudimentary "atom laser" that generates a beam of constant, m is the atomic mass and T is the temperature of coherent atoms, in analogy to emission of coherent the gas. At room temperature the de Broglie wavelength is photons by an optical laser. At the same time, theorists typically about ten thousand times smaller than the have clarified many fundamental issues and have de- average spacing between the atoms. This means that the veloped powerful methods to simulate real systems. matter waves of the individual atoms are uncorrelated or 30 Phy«tes World March 1997 "disordered", and the gas can cooling, polarization-gradient thus be described by classical cooling and magneto-optical Boltzmann statistics. trapping were developed to cool As the gas is cooled, however, and trap atoms. These techniques the smearing increases, and profoundly changed the nature of eventually there is more than atomic physics and provided a one atom in each cube of dimen- new route to ultracold tempera- sion ^.dB. The wavefunctions of tures that does not involve cryo- adjacent atoms then "overlap", genics. Atoms at sub-millikelvin causing the atoms to lose their temperatures are now routinely identity, and the behaviour of used in a variety of experiments. the gas is now governed by Alkali atoms are well suited to quantum statistics. laser-based methods because Bose-Einstein statistics dra- their optical transitions can be matically increase the chances of excited by available lasers and finding more than one atom in because they have a favourable the same state, and we can think internal energy-level structure for of the matter waves in a Bose cooling to low temperatures. gas as "oscillating in concert". However, the lowest temperat- The result is Bose—Einstein con- ure that these laser cooling tech- densation, a macroscopic occu- niques can reach is limited by the pation of the ground state of energy of a single photon. As a the gas. (In contrast, fermions - result, the "phase-space density" particles with a total spin of - the number of atoms within a l (n + /2)'h, where n is an integer - volume A.dB - is typically about a cannot occupy the same quan- million times lower than is tum state.) Einstein described needed for BEC. the process as condensation The successful route to BEC without interactions, making it turned out to be a marriage of an important paradigm of quan- the cooling techniques developed tum statistical mechanics. for hydrogen and those for the The density distribution of the alkalis: an alkali vapour is first condensate is represented by a laser cooled and then evapor- single macroscopic wavefunction atively cooled. In evaporative with a well denned amplitude and cooling, high-energy atoms are phase, just as for a classical field. allowed to escape from the sam- Indeed, the transition from dis- ple so that the average energy of ordered to coherent matter waves the remaining atoms is reduced. can be compared to the change Elastic collisions redistribute the from incoherent to laser light. energy among the atoms such Intensity (arbitrary units) that the velocity distribution Chilling the atoms reassumes a Maxwell-Boltzmann 2 Direct and non-destructive observation of the formation of form, but at a lower temperature. a Bose condensate by dispersive light scattering (phase- Bose-Einstein condensation has contrast Imaging) at MIT. The Intensity of scattered light is This is the same evaporation been cited as an important phe- shown as a function of position in the trap, which Is process that happens when tea nomenon in many areas of proportional to the column density of atoms along the line- cools, but the extra trick for physics, but until recently the of-sight. The Image on the left shows the cloud cooled to trapped atoms is that the thresh- only evidence for condensation just above the BEC transition temperature, and the old energy can be gradually came from studies of superfluid distribution of atoms is almost classical. As the temperature lowered. This allows the atomic is lowered through the phase transition a sharp peak of sample to be cooled by many liquid helium and excitons in atoms begins to appear at the trap centre (middle), and semiconductors. In the case of further cooling increases the condensate fraction to almost orders of magnitude, with the liquid helium, however, the 100% (right). only drawback being that the strong interactions that exist in a number of trapped atoms is liquid qualitatively alter the nature of the transition. For reduced {Physics Vforld 1995 July p21; August p21). this reason a long-standing goal in atomic physics has The challenge in combining these two cooling schemes been to achieve BEC in a dilute atomic gas. The challenge for alkalis was a question of atomic density. Optical was to cool the gases to temperatures around or below one methods work best at low densities, where the laser light is microkelvin, while preventing the atoms from condensing not completely absorbed by the sample. Evaporation, on into a solid or a liquid. the other hand, requires high atomic densities to ensure Efforts to Bose condense atoms began with hydrogen rapid rethermalization and cooling. This changed the more than 15 years ago. In these experiments hydrogen emphasis for optical methods: while they had previously atoms are first cooled in a dilution refrigerator, then been used to produce low temperatures and high phase- trapped by a magnetic field and further cooled by space density simultaneously, they now needed to produce evaporation (see below). This approach has come very high elastic collision rates. Furthermore, this had to be close to observing BEC, but is limited by the recombi- achieved in an ultrahigh vacuum chamber to prolong the nation of individual atoms to form molecules and by lifetime of the trapped gas. Thus no new concept was the detection efficiency. needed to achieve BEC, but rather it was an experimental In the 1980s laser-based techniques such as Doppler challenge to improve and optimize existing techniques. Phyaica Worid March 1997 31 These developments were pursued mainly at MIT and down states. The frequency of the field is adjusted so that Boulder from die early 1990s. it only affects the atoms at the edge of the cloud - in an harmonic oscillator potential, these atoms have the Improved techniques in magnetic trapping highest energy. When the moments of these atoms are flipped, the magnetic forces become anti-trapping and the For evaporative cooling to work, die atoms must be ther- atoms are expelled from the trap. As the cloud cools it mally isolated from their surroundings. This must be done shrinks towards the centre of the trap, so die frequency of with electromagnetic fields, since at ultracold temperat- the radio-frequency field must be continually reduced to ures atoms stick to all surfaces.