Quasi-1D Bose-Einstein condensates in the dimensional crossover regime
Résumé
We study theoretically the crossover from a three-dimensional elongated condensate to a one-dimensional condensate as thetransverse degrees of freedom get frozen by tight confinement. We compute analytically the radially integrated density profile at low temperatures usinga local density approximation, and study the behavior of phase fluctuations with the transverse confinement. Previous studies of phase fluctuations in trapped gases have either focused on the 3D elongated regimes or on the 1D regime. The presentapproach recovers these previous results and is able to interpolate between them. We show in particularthat the spatial correlation function of the matter wave field is insensitive to the transverse regime of confinement, pointing out an almost universal behavior of phase fluctuations in elongated traps.