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Physical Review A

Moment hierarchies and cumulants in quantum optics

Rüdiger Schack, Axel Schenzle

Published Apr 1, 1990• 42 citations
Publisher

Abstract

Nonlinear problems in quantum optics can be described by an infinite hierarchy of ordinary differential equations for the moments. We discuss different truncation schemes involving cumulants. For illustration the method is applied to second-harmonic generation. We prove that all but second-order cumulants are equal for any quasiprobability distribution ${\mathit{P}}_{\mathit{s}}$, especially for the P, Q, and W functions.

DOI
10.1103/physreva.41.3847

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Nonlinear problems in quantum optics can be described by an infinite hierarchy of ordinary differential equations for the moments. We discuss different truncation schemes involving cumulants. For illustration the method is applied to second-harmonic generation. We prove that all but second-order cumulants are equal for any quasiprobability distribution Ps{\mathit{P}}_{\mathit{s}}Ps​, especially for the P, Q, and W functions.
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