Quantum phase fluctuations and squeezing in degenerate four-wave mixing

We consider the generation of squeezed states in degenerate four-wave mixing, retaining all significant phase-matched terms in the third-order polarization. It is shown that, for output modes combined with appropriate phase shifts, ideal squeezed states are produced when the pump field is treated classically. An approximation scheme is used to investigate the effect of pump-field quantization. We show that for reasonable crystal lengths, the effect of pump-field quantization is insignificant in the region of significant squeezing.