Variational HFB Equations in the Thomas-Fermi Limit for Ultracold Trapped Gases

TL;DR

This paper derives simplified variational HFB equations for trapped Bose gases at finite temperature in the Thomas-Fermi limit, providing insights into density distributions that align qualitatively with experimental observations.

Contribution

It introduces a variational derivation of HFB equations in the Thomas-Fermi limit, simplifying the analysis of density profiles in trapped Bose gases.

Findings

Non condensate and anomalous densities peak at trap center

Results qualitatively match experimental data

Simplified expressions for densities in the Thomas-Fermi limit

Abstract

We derive variationally the HFB equations for a trapped self-interacting Bose gas at finite temperature. In the Thomas-Fermi limit, we obtain simple expressions for the condensate, the non condensate and the anomalous densities. Their behavior in terms of the condensate fraction meets qualitatively the experimental data. In particular, the non condensate and the anomalous densities are peaked at the center of the trap and not at the edges as predicted by the self-consistent HFB calculations.