Hydrodynamic modes of a 1D trapped Bose gas

TL;DR

This paper analyzes the hydrodynamic modes of a trapped Bose gas in one dimension, using both mean field and Lieb-Liniger models, providing analytical solutions and confirming recent sum rule results.

Contribution

It introduces a method to analytically determine collective mode frequencies for 1D Bose gases in different regimes, bridging mean field and Lieb-Liniger descriptions.

Findings

Excellent agreement with sum rule approach results

Analytical solutions for collective mode frequencies

Applicable to both mean field and Lieb-Liniger regimes

Abstract

We consider two regimes where a trapped Bose gas behaves as a one-dimensional system. In the first one the Bose gas is microscopically described by 3D mean field theory, but the trap is so elongated that it behaves as a 1D gas with respect to low frequency collective modes. In the second regime we assume that the 1D gas is truly 1D and that it is properly described by the Lieb-Liniger model. In both regimes we find the frequency of the lowest compressional mode by solving the hydrodynamic equations. This is done by making use of a method which allows to find analytical or quasi-analytical solutions of these equations for a large class of models approaching very closely the actual equation of state of the Bose gas. We find an excellent agreement with the recent results of Menotti and Stringari obtained from a sum rule approach.