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Beyond the Fokker-Planck equation: Stochastic Simulation of Complete Wigner representation for the Optical Parametric Oscillator

L. I. Plimak·M. K. Olsen·M. Fleischhauer·M. J. Collett
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Abstract

We demonstrate a method which allows the stochastic modelling of quantum systems for which the generalised Fokker-Planck equation in the phase space contains derivatives of higher than second order. This generalises quantum stochastics far beyond the quantum-optical paradigm of three and four-wave mixing problems to which these techniques have so far only been applicable. To verify our method, we model a full Wigner representation for the optical parametric oscillator, a system where the correct results are well known and can be obtained by other methods.

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L. I. Plimak, M. K. Olsen, M. Fleischhauer, M. J. Collett. 2001-08-29. Beyond the Fokker-Planck equation: Stochastic Simulation of Complete Wigner representation for the Optical Parametric Oscillator. https://doi.org/10.1209/epl/i2001-00529-8

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