Quantum optics of a Bose-Einstein condensate coupled to a quantized light field

We consider the interaction between a Bose-Einstein condensate and a single -mode quantized light field in the presence of a strong far-off-resonant pu mp laser. The dynamics is characterized by an exponential instability, henc e the system acts as an atom-photon parametric amplifier. Triggered by a sm all injected probe field, or simply by quantum noise, entangled atom-photon pairs are created which exhibit nonclassical correlations similar to those seen between photons in the optical parametric amplifier. In addition, the quantum statistics of the matter and light field depend strongly on the in itial state which triggers the amplifier. Thus, by preparing different init ial states of the light field, one can generate matter waves in a variety o f quantum states, demonstrating optical control over the quantum statistics of matter waves. [S1050-2947(99)06708-6].