Depletion and fluctuations of a trapped dipolar Bose-Einstein condensate in the roton regime

We consider the non-condensate density and density fluctuations of a trapped dipolar Bose-Einstein condensate, focusing on the regime where a roton-like excitation spectrum develops. Our results show that a characteristic peak in the non-condensate density occurs at trap center due to the rotons. In this regime we also find that the anomalous density becomes positive and peaked, giving rise to enhanced density fluctuations. We calculate the non-condensate density in momentum space and show that a small momentum halo is associated with the roton excitations.