Squeezing with phase diffusion in parametric amplifiers

We calculate the squeezing or quadrature spectrum of a nondegenerate parametric amplifier in an interferometer. Squeezing is found to occur below and above threshold. The new feature in the above threshold behavior is the existence of spontaneous phase diffusion in the transmitted signal, even with a stable pump. A novel technique is developed to calculate the quadrature fluctuations in the presence of phase diffusion. We find that squeezing occurs but is restricted to relatively high frequencies due to the phase diffusion. Another application of our theory is in the case of a subharmonic oscillator with a phase-diffusing pump. Squeezing is maintained here also, except at low frequencies. The presence of phase diffusion in quadrature phase sensitive detection can be expected to be universal. In all cases it tends to reduce or destroy the low-frequency squeezing and thereby increases low-frequency noise in a phase sensitive measurement. Our new stochastic technique, therefore, has a wide range of uses.