  A Bose-Einstein condensate of ultracold atoms inside the field of a
laser-driven optical cavity exhibits dispersive optical bistability. We
describe this system by using mean-field approximation and by analyzing the
correlation functions of the linearized quantum fluctuations around the
mean-field solution. The entanglement and the statistics of the atom-field
quadratures are given in the stationary state. It is shown that the mean-field
solution, i.e. the Bose-Einstein condensate is robust against entanglement
generation for most part of the phase diagram.
