Volume 56, Number 3, November 2001
|Page(s)||372 - 378|
|Section||Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics|
|Published online||01 December 2003|
Beyond the Fokker-Planck equation: Stochastic simulation of complete Wigner representation for the optical parametric oscillator
Department of Physics, University of Auckland Private Bag
92019, Auckland, New Zealand
2 Department of Chemical Physics, The Weizmann Institute of Science 76100 Rechovot, Israel
3 Fachbereich Physik, Universität Kaiserslautern D-67663 Kaiserslautern, Germany
4 Instituto de Física, Universidade Federal Fluminense Av. Litorânea s/n, Boa Viagem CEP 24210-340, Niterói, RJ, Brazil
Accepted: 6 August 2001
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.
PACS: 42.50.Lc – Quantum fluctuations, quantum noise, and quantum jumps / 02.50.Ey – Stochastic processes / 02.60.Cb – Numerical simulation; solution of equations
© EDP Sciences, 2001
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