Condensate fraction and critical temperature of a trapped interacting Bose gas

TL;DR

This paper uses a mean field approach to analyze how interactions affect the condensate fraction and critical temperature of a trapped Bose gas, revealing significant deviations from non-interacting models and providing an analytic expression for temperature shift.

Contribution

It introduces a mean field method based on the Popov approximation to quantify interaction effects on Bose gas condensation in traps, including an analytic temperature shift formula.

Findings

Repulsive interactions decrease condensate fraction and critical temperature.

The effects differ from those in homogeneous gases.

An analytic expression for the critical temperature shift is derived.

Abstract

By using a mean field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the non-interacting model. These effects go in the opposite direction compared to the case of a homogeneous gas. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived.