Semiclassical theory of the quasi two-dimensional trapped Bose gas

TL;DR

This paper develops a semiclassical approach to describe the density profile of a quasi two-dimensional trapped Bose gas, showing it aligns well with Quantum Monte Carlo results above the Kosterlitz--Thouless temperature, and highlighting differences from 2D mean-field theory.

Contribution

The paper introduces a semiclassical theory that accurately models the density profile of quasi 2D Bose gases, surpassing traditional 2D mean-field predictions in the normal phase.

Findings

Semiclassical theory matches Quantum Monte Carlo results above T_KT.

Differences observed between semiclassical and 2D mean-field predictions.

Relevance for analyzing ultra-cold-atom experiments in quasi 2D traps.

Abstract

We discuss the quasi two-dimensional trapped Bose gas where the thermal occupation of excited states in the tightly confined direction is small but remains finite in the thermodynamic limit. We show that the semiclassical theory describes very accurately the density profile obtained by Quantum Monte Carlo calculations in the normal phase above the Kosterlitz--Thouless temperature T_KT, but differs strongly from the predictions of strictly two-dimensional mean-field theory, even at relatively high temperature. We discuss the relevance of our findings for analyzing ultra-cold-atom experiments in quasi two-dimensional traps.