The time-dependent, linearly driven Fokker-Planck equation for the degenerate parametric amplifier is derived when the pump depletion is present both above and below threshold. A model that the driving force εα<sub>1</sub> is a product of the classical quantity ε and quantum operator α<sub>1</sub> is proposed. It is found that below or near threshold, our results conform to the linear theory or perturbation series expansion, and above threshold, the short-time behavior of our solution is close to the linearization approximation; with the increase of interaction time τ, the long-time behavior of our solution shows that the squeezing is always quite different from the linear theory. It is shown that the maximal squeezing can be obtained at large pump parameter μ=ε/k and interaction time Δτ.
© 2006 Optical Society of America
Original Manuscript: October 20, 2005
Revised Manuscript: June 24, 2006
Manuscript Accepted: July 11, 2006
Chaoying Zhao and Weihan Tan, "Quantum fluctuations in the time-dependent linearly driven degenerate parametric amplifier," J. Opt. Soc. Am. B 23, 2174-2179 (2006)