Collective modes of a harmonically trapped one-dimensional Bose gas: the effects of finite particle number and nonzero temperature

TL;DR

This paper develops a generalized Bogoliubov theory for a one-dimensional trapped Bose gas, analyzing how finite particle number and temperature influence collective modes across different interaction regimes, and compares results with recent experiments.

Contribution

It introduces a density functional approach using Lieb-Liniger solutions to study collective modes at finite temperature and particle number, extending previous models.

Findings

Finite particle number and temperature significantly affect collective mode frequencies.

Theoretical predictions do not fully match recent experimental data.

The model covers all interaction regimes from ideal to strongly interacting.

Abstract

Following the idea of the density functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap, by using a local chemical potential - calculated with the Lieb-Liniger exact solution - as the exchange energy. At zero temperature, we use the theory to describe collective modes of a finite-particle system in all interaction regimes from the ideal gas limit, to the mean-field Thomas-Fermi regime, and to the strongly interacting Tonks-Girardeau regime. At finite temperature, we investigate the temperature dependence of collective modes in the weak-coupling regime by means of a Hartree-Fock-Bogoliubov theory with Popov approximation. By emphasizing the effects of finite particle number and nonzero temperature on collective mode frequencies, we make comparisons of our results with the recent experimental measurement [E. Haller et al., Science 325, 1224 (2009)] and some previous theoretical predictions. We show that the experimental data are still not fully explained within current theoretical framework.