Dynamic structure factor and momentum distribution of a trapped Bose gas -art. no. 063608

The dynamic structure factor of a trapped Bose-Einstein condensed gas is in vestigated at zero temperature in the framework of Bogoliubov theory. Diffe rent values of momentum transfer are considered, ranging from the phonon to the single-particle regime. Various approximate schemes are discussed, inc luding the local density approximation, where the system is locally describ ed as a uniform gas, and the impulse approximation; in which the response i s fined by the momentum distribution of the condensate. A comprehensive app roach, based on the eikonal expansion, is presented. The predictions of the ory are successfully compared with the results of recent two-photon Bragg s cattering experiments, at both low and high momentum transfer. Relevant fea tures of the dynamic structure factor are also discussed using the formalis m of sum rules and the concept of scaling. Particular emphasis is given to the regime of high momentum transfer, in which the dynamic structure factor is sensitive to the behavior of the order parameter in momentum space, and some instructive examples showing the consequence of long-range coherence are presented.