Europhys. Lett.
Volume 66, Number 6, June 2004
Page(s) 771 - 777
Section General
Published online 01 June 2004
Europhys. Lett., 66 (6) , pp. 771-777 (2004)
DOI: 10.1209/epl/i2004-10035-7

Quasi-1D Bose-Einstein condensates in the dimensional crossover regime

F. Gerbier

Laboratoire Charles Fabry de l'Institut d'Optique - 91403 Orsay, France

(Received 27 January 2004; accepted in final form 31 March 2004)

We study theoretically the dimensional crossover from a three-dimensional elongated condensate to a one-dimensional condensate as the transverse degrees of freedom get frozen by tight confinement, in the limit of small density fluctuations, i.e. for a strongly degenerate gas. We compute analytically the radially integrated density profile at low temperatures using a 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 present approach recovers these previous results and is able to interpolate between them. We show in particular that in this strongly degenerate limit the shape of the spatial correlation function is insensitive to the transverse regime of confinement, pointing out to an almost universal behavior of phase fluctuations in elongated traps.

03.75.Hh - Static properties of condensates; thermodynamical, statistical and structural properties.
03.75.Gg - Entanglement and decoherence in Bose-Einstein condensates.

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