I'm going to give a remarkably unhelpful answer. Namely: shouldn't this be straightforward using the techniques of quantum optics? Unfortunately, I don't know quantum optics well enough to solve this easily, nor do I know of any references on quantum optics which are written for mathematicians (Please, if anybody knows one, tell me. If not, somebody please write one.).

I'm going to give a remarkably unhelpful answer. Namely: shouldn't this be a straightforward (although rather ugly) calculation using the techniques of quantum optics? Unfortunately, I don't know quantum optics well enough to solve this easily, nor do I know of any references on quantum optics which are written for mathematicians (Please, if anybody knows one, tell me. If not, somebody please write one.).