Quantum fluctuations and entanglement in the collective atomic recoil laser using a Bose-Einstein condensate

A complete quantum description of the collective atomic recoil laser, in which a Bose-Einstein condensate driven by a detuned laser field is coupled to a single-mode quantized radiation field is presented. The temporal evolution of the Heisenberg operators and the state when the system starts from vacuum is calculated. As a result, the calculation of the evolution of the state allows for a detailed description of the entanglement between atoms and photons.