Two point correlations of a trapped interacting Bose gas at finite temperature

TL;DR

This paper introduces a computational method combining classical field and Hartree-Fock approaches to calculate finite temperature correlation functions of trapped Bose gases, aligning with experimental capabilities.

Contribution

A novel hybrid computational approach for finite temperature correlation functions in trapped Bose gases that includes s-wave interactions and is applicable near the critical temperature.

Findings

Calculated first and second order correlation functions in position and momentum space.

Characterized the spatial coherence length of the Bose gas.

Results are relevant for experimental measurements near the critical temperature.

Abstract

We develop a computationally tractable method for calculating correlation functions of the finite temperature trapped Bose gas that includes the effects of s-wave interactions. Our approach uses a classical field method to model the low energy modes and treats the high energy modes using a Hartree-Fock description. We present results of first and second order correlation functions, in position and momentum space, for an experimentally realistic system in the temperature range of $0.6T_c$ to $1.0T_c$. We also characterize the spatial coherence length of the system. Our theory should be applicable in the critical region where experiments are now able to measure first and second order correlations.