Quasi One-Dimensional Bosons in Three-dimensional Traps: From Strong Coupling to Weak Coupling Regime

TL;DR

This paper examines a recent experiment on 87Rb atoms in a quasi-one-dimensional trap, comparing experimental data with theoretical models and exploring different regimes of the gas's behavior.

Contribution

It introduces a theory accounting for transverse width variations, improving the description of the experimental data over previous one-dimensional models.

Findings

Experimental data align with Lieb et al.'s 1D theory but are better explained by a transverse width variation model.

The study investigates free axial expansion in various regimes: Tonks-Girardeau, 1D BEC, and 3D BEC.

Theoretical analysis enhances understanding of dimensional crossover in trapped bosonic gases.

Abstract

We analyze a recent experiment on a Tonks-Girardeau gas of $^{87}$Rb atoms (T. Kinoshita, T. Wenger, and D.S. Weiss, Science {\bf 305}, 1125 (2004)). We find that the experimental data are compatible with the one-dimensional theory of Lieb, Seiringer and Yngvason (Phys. Rev. Lett. {\bf 91}, 150401 (2003)) but are better described by a theory that takes into account variations in the transverse width of the atomic cloud. By using this theory we investigate also the free axial expansion of the $^{87}$Rb gas in different regimes: Tonks-Girardeau gas, one-dimensional Bose-Einstein condensate and three-dimensional Bose-Einstein condensate.