Dynamic structure factor and momentum distribution of a trapped Bose gas

TL;DR

This paper investigates the dynamic structure factor of a trapped Bose-Einstein condensate at zero temperature across various momentum regimes, comparing theoretical predictions with experimental results and exploring the effects of long-range coherence.

Contribution

It introduces a comprehensive theoretical framework using Bogoliubov theory and eikonal expansion to analyze the dynamic structure factor in different regimes, including high momentum transfer.

Findings

Theoretical predictions agree with recent Bragg scattering experiments.

High momentum transfer reveals sensitivity to the condensate's order parameter in momentum space.

Long-range coherence influences the dynamic structure factor significantly.

Abstract

The dynamic structure factor of a trapped Bose-Einstein condensed gas is investigated at zero temperature in the framework of Bogoliubov theory. Different values of momentum transfer are considered, ranging from the phonon to the single-particle regime. Various approximated schemes are discussed, including the local density approximation, where the system is locally described as a uniform gas, and the impulse approximation, where the response is fixed by the momentum distribution of the condensate. A comprehensive approach, based on the eikonal expansion, is presented. The predictions of theory are successfully compared with the results of recent two-photon Bragg scattering experiments, both at low and high momentum transfer. Relevant features of the dynamic structure factor are also discussed using the formalism of sum rules and the concept of scaling. Particular emphasis is given to the regime of high momentum transfer, where the dynamic structure factor is sensitive to the behaviour of the order parameter in momentum space, and some instructive examples showing the consequence of long-range coherence are presented.