Thermodynamics of a trapped Bose-condensed gas

TL;DR

This paper develops a mean field theoretical framework for analyzing the thermodynamics of a trapped Bose-condensed gas at finite temperature, revealing significant effects of interactions and boundary states on its behavior.

Contribution

It introduces a generalized Bogoliubov mean field approach combined with WKB approximation to systematically study thermodynamic properties of trapped Bose gases.

Findings

Thermal depletion of the condensate is enhanced by repulsive interactions.

Critical temperature decreases compared to non-interacting models.

System exhibits a scaling behavior in the large N limit.

Abstract

We investigate the thermodynamic behaviour of a Bose gas interacting with repulsive forces and confined in a harmonic anisotropic trap. We develop the formalism of mean field theory for non uniform systems at finite temperature, based on the generalization of Bogoliubov theory for uniform gases. By employing the WKB semiclassical approximation for the excited states we derive systematic results for the temperature dependence of various thermodynamic quantities: condensate fraction, density profiles, thermal energy, specific heat and moment of inertia. Our analysis points out important differences with respect to the thermodynamic behaviour of uniform Bose gases. This is mainly the consequence of a major role played by single particle states at the boundary of the condensate. We find that the thermal depletion of the condensate is strongly enhanced by the presence of repulsive interactions and that the critical temperature is decreased with respect to the predictions of the non-interacting model. Our work points out an important scaling behaviour exhinited by the system in large $N$ limit. Scaling permits to express all the relevant thermodynamic quantities in terms of only two parameters: the reduced temperature $t=T/T_c^0$ and the ratio between the $T=0$ value of the chemical potential and the critical temperature $T_c^0$ for Bose-Einstein condensation. Comparisons with first experimental results and ab-initio calculations are presented.