Nucleation of Bose-Einstein condensation

Using a functional formulation of the Keldysh theory we investigate the time evolution of a dilute Bose gas through the critical point. We determine the critical region of the gas and show that if the system is quenched inside this region, Bose-Einstein condensation is nucleated on a time scale of O({}/kB{T}c$) by means of a coherent population of the one-particle ground state. We also examine the subsequent buildup of the condensate density, taking place on a much longer time scale. However, in the experimentally interesting case of spin-polarized atomic hydrogen or cesium it is still short compared to the lifetime of the gas.