  We develop a fully quantized model of a Bose-Einstein condensate driven by a
far off-resonant pump laser which interacts with a single mode of an optical
ring cavity. In the linear regime, the cavity mode exhibits spontaneous
exponential gain correlated with the appearance of two atomic field side-modes.
These side-modes and the cavity field are generated in a highly entangled
state, characterized by thermal intensity fluctuations in the individual modes,
but with two-mode correlation functions which violate certain classical
inequalities. By injecting an initial coherent field into the optical cavity
one can significantly decrease the intensity fluctuations at the expense of
reducing the correlations, thus allowing for optical control over the quantum
statistical properties of matter waves.
