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

Atomic diffraction by a laser stationary wave is commonly used to build mir rors and beam splitters for atomic interferometers. Many aspects of this di ffraction process are well understood but it is difficult to get an unified view of this process because it is commonly described in several approxima te ways. We want to show here that a description inspired by optics and usi ng 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 forma lism. In order to get simple analytic expressions of the diffraction amplit udes, we consider a standing wave intensity with a flat transverse profile. The resulting general expression of the diffraction intensities is then co mpared to available analytical formulae in the Raman-Nath limit and in the Bragg regime. We think that this formalism can be fruitfully extended to st udy many important questions.