Local-field approach to the interaction of an ultracold dense Bose gas with a light field

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Abstract
The propagation of the electromagnetic field of a laser through a dense Bose gas is examined and nonlinear operator equations for the motion of the center of mass of the atoms are derived. The goal is to present a self-consistent set of coupled Maxwell-Bloch equations for atomic and electromagnetic fields generalized to include the atomic center-of-mass motion. Two effects are considered: The ultracold gas forms a medium for the Maxwell field which modifies its propagation properties. Combined herewith is the influence of the dipole-dipole interaction between atoms which leads to a density dependent shift of the atomic transition frequency. It is expressed in a position dependent detuning and is the reason for the nonlinearity. This results in a direct and physically transparent way from the quantum field theoretical version of the local-field approach to electrodynamics in quantum media. The equations for the matter fields are general. Previously published nonlinear equations are obtained as limiting cases. As an atom optical application the scattering of a dense beam of a Bose gas is studied in the Raman-Nath regime. The main conclusion is that for increasing density of the gas the dipole-dipole interaction suppresses or enhances the scattering depending on the sign of the detuning.

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