2 9 M ar 2 00 5 Bose - Einstein condensation

Bose-Einstein condensation is the occupation of a single quantum state by a large number of identical particles. This implies that particles are assumed to be bosons, satisfying the Bose-Einstein statistics allowing for many particles to pile up in the same quantum state. This is contrary to fermions, satisfying the Fermi-Dirac statistics, for which the Pauli exclusion principle does not allow the occupation of any single quantum state by more than one particle. The role of quantum correlations, caused by the Bose-Einstein statistics, is crucial for the occurrence of BEC. This statistics was advanced by Bose (1924) for photons, having zero mass, and generalized by Einstein (1924) to particles with nonzero masses. Einstein (1925) also described the phenomenon of condensation in ideal gases. The possibility of BEC in weakly nonideal gases was theoretically demonstrated by Bogolubov (1947). The wave function of Bose-condensed particles in dilute gases satisfies the Gross-Pitaevskii equation, suggested by Gross (1961) and Pitaevskii (1961). Its mathematical structure is that of the nonlinear Schrödinger equation. Experimental evidence of BEC in weakly interacting confined gases was achieved, seventy years after the Einstein prediction, almost simultaneously by three experimental groups (Anderson et al., 1995; Bradley et al., 1995; Davis et al., 1995). To say that many particles are in the same quantum state is equivalent to saying that these particles display the state coherence. That is, BEC is a particular case of coherence phenomena related to the arising state coherence. For the latter to occur, the particles are to be strongly correlated with each other. The expected conditions, when such a strong correlation could appear, may be qualitatively understood applying the de Broglie duality arguments to an ensemble of atoms in thermodynamic equilibrium at temperature T . Then the thermal energy of an atom is given by kBT , where kB is the Boltzmann constant. This energy defines the thermal wavelength