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 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.