Particle number fluctuations in a cloven trapped Bose gas at finite temperature

TL;DR

This paper analyzes atom number fluctuations in a trapped Bose gas at finite temperature, providing analytical solutions and identifying a temperature where fluctuations peak due to interference effects.

Contribution

It offers analytical solutions for fluctuations in both non-interacting and interacting Bose gases, including in the Thomas-Fermi and high-temperature limits, validated by classical field simulations.

Findings

Fluctuations peak at approximately 0.7 T_c regardless of trap anisotropy.

Analytical solutions match classical field simulation results.

Maximum fluctuations result from interference between condensate and non-condensed fields.

Abstract

We study fluctuations in the atom number difference between two halves of a harmonically trapped Bose gas in three dimensions. We solve the problem analytically for non interacting atoms. In the interacting case we find an analytical solution in the Thomas-Fermi and high temperature limit in good agreement with classical field simulations. In the large system size limit, fluctuations in the number difference are maximal for a temperature $T\simeq 0.7 T_c$ where $T_c$ is the critical temperature, independently of the trap anisotropy. The occurrence of this maximum is due to an interference effect between the condensate and the non-condensed field.