Precision Monte Carlo Test of the Hartree-Fock Approximation for a trapped Bose Gas

TL;DR

This paper compares the Hartree-Fock approximation to Path Integral Quantum Monte Carlo simulations for a trapped Bose gas, revealing corrections to density profiles and increased condensed particles, with implications for current Rb experiments.

Contribution

It provides a precise Monte Carlo validation of the Hartree-Fock approximation for trapped Bose gases, highlighting corrections and experimental observability.

Findings

Corrections to mean-field density profiles observed.

Increase in condensed particles consistent with homogeneous systems.

Proposed method for analyzing in-situ experimental data.

Abstract

We compare the semiclassical Hartree-Fock approximation for a trapped Bose gas to a direct Path Integral Quantum Monte Carlo simulation. The chosen parameters correspond to current Rb experiments. We observe corrections to the mean-field density profile. The Path Integral calculation reveals an increase of the number of condensed particles, which is of the same order as a previously computed result for a homogeneous system. We discuss the experimental observability of the effect and propose a method to analyze data of in-situ experiments.