Bose-Einstein condensation

Bosons are particles with an integer spin: S=0, 1, etc. Fermions are particles with a half-integer spin: S=1/2, 3/2, etc., e.g., electrons have S=1/2. An arbitrary number of bosons can occupy the same quantum state (e.g., when all photons in a laser beam have identical energies and polarization, and move in exactly the same direction), whereas no more than one fermion can be found in a given quantum state (this is known as the Pauli exclusion principle). As the temperature is lowered a system of bosons may undergo a transition into the Bose-Einstein condensate state. In this state a finite fraction of the number of particles occupies the lowest energy state, i.e., a macroscopic number of particles are described by the same wave function corresponding to this state. This leads to observable effects. For example, when such condensate moves as a whole, this motion can proceed without dissipation of energy, which means superfluidity.

Recent experiments on BEC [Science, 269(5221), 198 (1995); Phys. Rev. Lett. 75, 3969 (1995); 77, 4984 (1996)] were performed with atomic gases in traps, where atoms are held together by the magnetic field and cooled down to nano-Kelvin temperatures using laser and evaporative cooling. The trapped atoms are characterized by some momentum distribution, whose width is determined by the temperature of the gas. When the Bose-Einstein transition takes place, the momentum distribution suddenly narrows, which means that a large number of atoms now occupy the lowest energy state. Until these experiments the BEC was observed only in condensed state systems (liquid He), where atoms interact strongly with each other. The recent achievement is remarkable because the BEC is obtained in the gas phase, where the interaction between atoms is relatively small. However, this interaction is crucial for the formation of the condensate. According to the standard theoretical picture of the BEC, the condensate is possible only when the atoms repel each other. Microscopically, this means that the atom-atom scattering length must be positive. If the atom-atom scattering length is negative, the atoms attract each other and a stable BEC is not possible. In spite of this notion, it was claimed recently [Phys. Rev. Lett. 75, 1687 (1995); 78, 985 (1997)] that BEC also takes place in the gas of lithium atoms, where the scattering length is negative. So far there has been no unambiguous interpretation of this result.

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