Exploring the growth of correlations in a quasi one-dimensional trapped Bose gas

TL;DR

This paper investigates the development of correlations in a quasi one-dimensional trapped Bose gas, using extended mean-field theory and analytical methods to explore different interaction regimes and compare with exact solutions.

Contribution

It provides a comprehensive analysis of correlation functions up to third order, bridging the gap between weakly and strongly correlated regimes in trapped Bose gases.

Findings

Good agreement with Lieb-Liniger solution in the homogeneous limit

Characterization of the transition from Gross-Pitaevskii to Tonks-Girardeau regimes

Evaluation of phase correlations and density fluctuations at finite temperature

Abstract

Phase correlations, density fluctuations and three-body loss rates are relevant for many experiments in quasi one-dimensional geometries. Extended mean-field theory is used to evaluate correlation functions up to third order for a quasi one-dimensional trapped Bose gas at zero and finite temperature. At zero temperature and in the homogeneous limit, we also study the transition from the weakly correlated Gross-Pitaevskii regime to the strongly correlated Tonks-Girardeau regime analytically. We compare our results with the exact Lieb-Liniger solution for the homogeneous case and find good agreement up to the cross-over regime.