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

We compare the semiclassical Hartree-Fock approximation for a trapped Bose gas to a direct path-integral quantum Monte Carlo simulation. The chosen pa rameters correspond to current Rb-87 experiments. We observe corrections to the mean-field density profile: the path-integral calculation reveals an i ncrease of the number of condensed particles, which is of the same order as a previously computed result for a homogeneous system. We discuss the expe rimental observability of the effect and propose a method to analyze data o f in situ experiments. [S1050-2947(99)02404-X].