Second-quantized effective models for Raman diffraction with center-of-mass motion

Abstract

Two-photon Raman transitions are commonly used to facilitate π/2- and π-pulses in atom interferometry, and are the analogue of beam splitters and mirrors in optical interferometers. In practice, these transitions are driven by laser light which can be described semi-classically as quasi-coherent states. Thus quantization effects are averaged out due to the broad photon distribution in typical beams. However, technological progress moves towards the use of optical cavities due to their superior optical properties. Theoretical modeling of such configurations demands a second-quantized description of the light fields which we pursue based on the light-matter interaction of two second-quantized single-mode light fields and an effective two-level atom. In this thesis we derive and investigate a two-photon Rabi model with center-of-mass motion including intensity-dependent operator-valued couplings between the light field and the center-of-mass motion. We show, that under certain approximations we obtain an effective Jaynes-Cummings model with a center-of-mass dependent detuning.