Limitations of entanglement between photons and atoms coupled out from a Bose-Einstein condensate

We study the limitations on the relative number squeezing between photons and atoms coupled out from a homogeneous Bose-Einstein condensate. We consider the coupling between the translational atomic states by two photon Bragg processes, with one of the photon modes involved in the Bragg process in a coherent state and the other initially unpopulated. We start with an interacting Bose condensate at zero temperature and compute the time evolution for the system. We study the squeezing, i.e., the variance of the occupation number difference between the second photon and the atomic center-of-mass mode. We discuss how collisions between the atoms and photon rescattering affect the degree of squeezing which may be reached in such experiments.