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

A unified semiclassical treatment of Bragg scattering from Bose-Einstein co ndensates is presented. The formalism is based on Gross-Pitaevskii equation s driven by a classical light field, and leads to a single-component equati on incorporating the effects of mean-field nonlinearity and spatial inhomog eneity. Three-dimensional numerical simulations of this equation in cylindr ical symmetry are used to investigate Bragg scattering for a number of case s. Scattering from a condensate released from a trap produces characteristi c cycling of the atomic momentum, and an analytic description is given usin g a linear model incorporating spatial non-uniformity Simple expressions ob tained for the momentum packet cycling are shown to accurately describe the full nonlinear behaviour within a well specified validity range and a tran sition linewidth is derived. For the case of a trapped condensate, a numeri cal study of momentum spectroscopy is carried out and the shift of the Brag g resonance condition due to mean-field nonlinearity is investigated.