The density matrix in the Wigner representation has been widely used in problems related to the recoil effect and laser cooling. For some mysterious reason it hasn’t used in much in problems involving atom interferometry. Of course there are hundreds of articles (maybe more) and books on the Wigner representation; however here we are concerned mainly with its application to calculations involving atom interferometry. The only examples we know of are the ones referred to in the paper.
Two processes are considered, one occurs during the interaction between the cold atom cloud and the Raman beams, the other occurs during the free evolution of the cold atom cloud in vacuum.