Precision Monte Carlo test of the Hartree-Fock approximation for a trapped Bose gas

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 ⁸⁷Rb 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.