Diffraction effects on light-atomic-ensemble quantum interface

We present a simple method to include the effects of diffraction into the description of a light-atomic ensemble quantum interface in the context of collective variables. Carrying out a scattering calculation we single out the purely geometrical effect and apply our method to the experimental relevant case of Gaussian-shaped atomic samples stored in single beam optical dipole traps probed by a Gaussian beam. We derive simple scaling relations for the effect of the interaction geometry and compare our findings to the results from one-dimensional models of light propagation.