Matter waves in new quantum regime.

David Meacher and Peter Ruprecht
Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK.
A version of this article appeared in Physics World, p. 21, August 1995.

The phenomenon of Bose-Einstein condensation (BEC), first predicted by Einstein seventy years ago but whose direct observation has hitherto defied the ingenuity of researchers, has finally been seen in the laboratory. In experiments reported recently by Anderson et al. (Science, 14 July 1995, p. 198) and carried out at the Joint Institute for Laboratory Astrophysics of the University of Colorado at Boulder, a sample of gaseous rubidium atoms confined in a magnetic trap was cooled to a temperature of just a few nanoKelvin, less than a billionth of that of outer space, until the atoms condensed into the same quantum state. In the resulting condensate the concept of individual particles ceases to have meaning: the sample of gas behaves as a single entity, its quantum mechanical nature magnified up to the macroscopic domain.

According to quantum mechanics, particles at a temperature T can be represented by waves with a characteristic (deBroglie ) wavelength, . Whilst this and other predictions of quantum mechanics have been verified in experiments on microscopic systems such as atoms, purely quantum mechanical phenomena do not often intrude on the macroscopic world of our everyday experience. Nevertheless, quantum mechanics does make predictions about the behaviour of arbitrarily large assemblies of identical particles. In particular, strikingly different behaviour is expected depending on whether the particles concerned have half-integral or integral intrinsic angular momentum (in units of ). The former class of particles, known as fermions obey the Pauli exclusion principle. This effectively provides a force of quantum mechanical origin keeping such particles apart and is responsible for the stability of atoms and for the existence of the hierarchy of elements of the Periodic Table. For the second class of particles, the bosons, there is no restriction as to the number of particles that can occupy a given quantum state, and indeed the probability of a particle falling into a given state increases in proportion to the number of particles already occupying it. This can lead to BEC , an avalanche process which occurs when the particles are close enough for their wavefunctions to overlap, that is when there are several atoms per volume . This process is analogous to the stimulated emission that occurs in a laser cavity which results in photons, also bosons, being emitted into the same cavity mode. Just as in the laser beam the concept of individual photons is not appropriate, so in the condensate the concept of individual particles is meaningless. Thus, the sample must be treated as a single quantum mechanical entity: coherent matter.

The observation of BEC brings to fruition a struggle that has engaged researchers for many years. The difficulty arises from the fact that most of the bosons accessible to experimenters are atoms, which often have strong mutual interactions. The result is that as the density of the gas is increased to the level at which the wavefunctions start to overlap, the unwanted interactions completely dominate the quantum statistical effects or even cause loss of particles, for example through the formation of molecules. (It is this last effect which has stalled the push toward higher densities in atomic hydrogen, which several years ago seemed the prime candidate for the observation of BEC.) Although condensation phenomena are required to explain the superfluidity of liquid helium below the -point and superconductivity in metals, the macroscopic properties of these systems are dominated by interaction effects and thus the properties of the condensate are masked.

For this reason recent attempts to see BEC with atoms have concentrated on the use of dilute atomic gases with an inter-particle spacing large compared to the range of interatomic interactions. The condition that there should be several atoms in a volume of then translates to a requirement that the deBroglie wavelength be correspondingly long. This demands that the sample be cooled to a temperature unimaginably close to Absolute Zero.

In the experiments reported by Anderson et al., rubidium atoms are first optically cooled then loaded into a magnetic trap. The crucial advance in this experiment was the development of a new trap configuration which eliminated the principle cause of loss of particles from the sample. Its mode of operation is described in the July, 1995, edition of Physics World. Once the atoms were loaded into the trap they were further cooled by forced evaporation. This works by selectively ejecting the particles with higher than average energy from the trap, with the remaining atoms then undergoing elastic collisions leading to their rethermalization at a lower temperature. In this way the temperature may be reduced to the nK range at the cost only of a reduction in the number of atoms in the sample.

To demonstrate the formation of a Bose-Einstein condensate Anderson et al. studied the velocity distribution of the remaining trapped atoms after evaporative cooling. Because of the small size of the trapped cloud, which prevented direct imaging, they made these measurements by switching off the magnetic trap, thereby allowing the cloud to expand ballistically. Then, after an interval of time, they illuminated the expanded cloud with a brief pulse of laser light. The atoms partially absorbed the light, thereby imposing on the transmitted beam a shadow of the atomic density distribution, which was then recorded by a camera. The image obtained was a two-dimensional representation of the velocity distribution of the atoms at the moment of release. Figure 1a shows the image obtained for a temperature above that for which a condensate was formed. The symmetric circular shadow is indicative of an isotropic, thermal distribution of velocities. When the temperature was reduced below 170nK, however, images such as figure 1b were obtained. This shows, along with the symmetric halo of the uncondensed part of the atomic distribution, a bright, asymmetric central region corresponding to atoms with a very narrow, nonthermal, range of velocities.

There are compelling reasons to believe that this second image represents the first direct observation of BEC in a weakly coupled gas. Firstly, the population of the central peak increases rapidly as the temperature is decreased below threshold for BEC , consistent with the notion of bosons flooding into a single state. Secondly, the velocity distribution calculated from this image is very nearly that expected for the lowest vibrational state of the trapping potential. Its prolate form contrasts markedly with the symmetric form of the distribution of the uncondensed atoms and is strong evidence that it represents atoms originating in a single macroscopically-occupied quantum state, because an average over several trap states would give a more nearly isotropic distribution.

There is no doubt that the observation of BEC represents the dawn of a new era in the study of the properties of matter, just as the advent of the laser revolutionized our understanding of light and its technological applications. Possible new developments involving BEC include the manipulation of coherent matter waves, for applications ranging from determining fundamental constants to new methods of lithography and nanofabrication. Further rapid advances in this exciting field are to be expected as the properties of this new state of matter begin to be probed.

FIGURE CAPTIONS

Figure 1: Velocity distributions of the trapped and cooled atoms. (a) shows the isotropic thermal distribution before the onset of condensation. In (b), a very dense, elliptical, Bose-Einstein condensed fraction containing about 2000 atoms appears as the sample is cooled below the critical temperature.

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