We extend the quantum theory of nondegenerate four-wave mixing by including the effects of the finite bandwidth of the driving-pump field. The interaction of a beam of two-level atoms with the two opposite driving-pump fields that have finite bandwidth inside a bimodal cavity is considered. The master equation for the cavity-field modes, averaged over the stochastic process, is derived. We use our theory to study the effects of phase fluctuations, associated with the driving-pump field, on the generation of two-mode squeezing inside the cavity. The steady-state squeezing is achieved with the same driving-pump field as a local oscillator in the balanced homodyne-detection system. Our results show that, in spite of instantaneous phase locking between the cavity field and the local oscillator, the time-delay effects associated with the exponential decay of atomic coherence relate the steady-state squeezing to the diffusion constant of the driving-pump field.
© 1997 Optical Society of America
A. H. Toor and M. S. Zubairy, "Quantum theory of nondegenerate multiwave mixing: effect of pump phase fluctuations," J. Opt. Soc. Am. B 14, 1280-1288 (1997)