Pair correlation function of an inhomogeneous interacting Bose-Einstein condensate

We calculate the pair correlation function of an interacting Bose gas in a harmonic trap directly via Path Integral Quantum Monte-Carlo simulation for various temperatures and compare the numerical result with simple approximative treatments. Around the critical temperature of Bose-Einstein condensation, a description based on the Hartree-Fock approximation is found to be accurate. At low temperatures the Hartree-Fock approach fails and we use a local density approximation based on the Bogoliubov description for a homogeneous gas. This approximation agrees with the simulation results at low temperatures, where the contribution of the phonon-like modes affects the long range behavior of the correlation function. Further we discuss the relation between the pair correlation and quantities measured in recent experiments.