Quantum theory of optical feedback via homodyne detection

We present a quantum theory of feedback in which the homodyne photocurrent alters the dynamics of the source cavity. To the nonlinear stochastic (Ito) evolution of the conditioned system state we add a feedback term linear in the instantaneous stochastic (Stratonovich) photocurrent. Averaging over the photocurrent gives a feedbackk master equation which has the desired driftlike term, plus a diffusionlike term. We apply the model to phase locking a regularly pumped laser, and show that under ideal conditions the noise spectra of the output light exhibit perfect squeezing on resonance.