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.
A second example is the equation 9b for Wigner function: the associated quotation is ref. 17 by one of the authors and M.A. Kasevich in Phys Rev A (2006). A brief search on the web proves that a similar equation was used by Hongyi Fan Phys Rev A 656, 064102 (2002) who quotes two references dating from 1984 and a book published in 1994. I am not sufficiently aware of the use f Wigner function but I am sure that there are better and more useful references to quote in addition to ref 17!