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

TL;DR

This paper provides a theoretical analysis of the transition from three-dimensional to one-dimensional Bose-Einstein condensates under tight transverse confinement, revealing universal behavior of phase fluctuations across regimes.

Contribution

It introduces an analytical approach to interpolate between 3D and 1D regimes, highlighting the universality of phase fluctuation behavior in elongated traps.

Findings

Density profile computed analytically at low temperatures.

Phase fluctuations are insensitive to transverse confinement in the degenerate limit.

The approach unifies previous 3D and 1D studies of Bose-Einstein condensates.

Abstract

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.