Mean-field treatment of Bragg scattering from a Bose-Einstein condensate

A unified semiclassical treatment of Bragg scattering from Bose-Einstein condensates is presented. The formalism is based on Gross-Pitaevskii equations driven by a classical light field, and leads to a single-component equation incorporating the effects of mean-field nonlinearity and spatial inhomogeneity. Three-dimensional numerical simulations of this equation in cylindrical symmetry are used to investigate Bragg scattering for a number of cases. Scattering from a condensate released from a trap produces characteristic cycling of the atomic momentum, and an analytic description is given using a linear model incorporating spatial non-uniformity. Simple expressions obtained for the momentum packet cycling are shown to accurately describe the full nonlinear behaviour within a well specified validity range and a transition linewidth is derived. For the case of a trapped condensate, a numerical study of momentum spectroscopy is carried out and the shift of the Bragg resonance condition due to mean-field nonlinearity is investigated.