Atomic diffraction by a laser standing wave: Analysis using Bloch states

Atomic diffraction by a laser stationary wave is commonly used to build mirrors and beam splitters for atomic interferometers. Many aspects of this diffraction process are well understood but it is difficult to get an unified view of this process because it is commonly described in several approximate ways. We want to show here that a description inspired by optics and using the exact Bloch description of the atomic wave inside the laser standing wave is a tutorial way of describing the various regimes by a single formalism. In order to get simple analytic expressions of the diffraction amplitudes, we consider a standing wave intensity with a flat transverse profile. The resulting general expression of the diffraction intensities is then compared to available analytical formulae in the Raman-Nath limit and in the Bragg regime. We think that this formalism can be fruitfully extended to study many important questions