Entanglement in a Bose-Einstein condensate by collective atomic recoil

We address the interaction between a Bose-Einstein condensate and a single-mode quantized radiation field in the presence of a strong far off-resonant pump laser. The generation of atom-atom and atom-field entanglement is demonstrated in the linear regime. The effects of cavity losses are taken into account and an analytic solution of the corresponding master equation is given in terms of the Wigner function of the system.