Spatial Correlation Functions of one-dimensional Bose gases at Equilibrium

TL;DR

This paper investigates how the spatial correlation functions of a one-dimensional Bose gas at equilibrium depend on temperature and interaction strength, highlighting the importance of density fluctuations and providing new methods for analyzing condensate properties.

Contribution

It introduces a stochastic Langevin approach to analyze correlation functions, emphasizing the role of density fluctuations and offering an alternative to traditional density fitting methods.

Findings

Correlation functions change from Gaussian to exponential with temperature.

Density fluctuations significantly influence the coherence length.

Results align with existing theoretical predictions for higher order correlations.

Abstract

The dependence of the three lowest order spatial correlation functions of a harmonically confined Bose gas on temperature and interaction strength is presented at equilibrium. Our analysis is based on a stochastic Langevin equation for the order parameter of a weakly-interacting gas. Comparison of the predicted first order correlation functions to those of appropriate mean field theories demonstrates the potentially crucial role of density fluctuations on the equilibrium coherence length. Furthermore,the change in both coherence length and shape of the correlation function, from gaussian to exponential, with increasing temperature is quantified. Moreover, the presented results for higher order correlation functions are shown to be in agreeement with existing predictions. Appropriate consideration of density-density correlations is shown to facilitate a precise determination of quasi-condensate density profiles, providing an alternative approach to the bimodal density fits typically used experimentally.