Abstract

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 $\epsilon {\alpha }_1$ is a product of the classical quantity ε and quantum operator ${\alpha }_1$ 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 $\mu =\epsilon ∕k$ and interaction time $\Delta \tau$.

© 2006 Optical Society of America

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