Quantum simulations of nonlinear optical damping: An exact solution for the stochastic differential equations and an interpretation of ‘‘spiking’’

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Abstract
This paper considers the ‘‘positive-P’’ description of nonlinear optical damping where one-photon and two-photon loss mechanisms are allowed. An exact solution of the corresponding stochastic differential equations is presented that graphically shows the breakdown of the positive-P representation found in earlier numerical-simulation work. The problem of ‘‘spiking’’ in simulations of nonlinear optical processes is then addressed, using the nonlinear damping process as an example. It is pointed out that although ‘‘spiking’’ can be exascerbated at high levels of quantum noise by numerical inaccuracy, the tendency to spike is in fact an analytic property of the stochastic variables.

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