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Physical Review A

Quantum fluctuations in parametric down-conversion and their classical stochastic description

Dorota Kupiszewska, Kazimierz Rza̧żewski

Published Dec 1, 1990• 9 citations
Publisher

Abstract

Using a simple model of parametric down-conversion, we demonstrate the usefulness of the classical stochastic approximation of nonlinear quantum dynamics in the processes leading to a transient squeezing of initial vacuum fluctuations. We stress the importance of the Wigner function in the method.
DOI
10.1103/physreva.42.6869

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Nonlinear multiphoton conversion processes are theoretically and experimentally challenging systems in quantum optics and related areas. These phenomena bring remarkable quantum properties and can be of fundamental relevance in quantum information and computation applications. Based on recent experimental advances and the possible uses in generalized three-photon squeezing, we investigate degenerate three-photon parametric down-conversion generated inside a cavity fed by a classical pump. In addition, we consider that the process is stimulated by a coherent driving mode and subjected to dissipation by spontaneous emission of the cavity. A treatment using phase-space methods and stochastic differential equations is applied and the stability conditions of its steady states are found. We find that the system does not exhibit multistability, instead it has a limited parameter region leading to a single stable steady branch, alongside multiple unstable branches. Focusing on the stable steady states and linearizing the dynamics around them, we calculate the spectral densities of the quadrature variables. We identify and characterize the squeezing of three-photon down-conversion. Moreover, since the quasi-probability differential equations of the higher-order multiphoton processes have higher-order derivatives, hindering their mapping into stochastic differential equations, we make use of a positive Wigner function approach to calculate two-dimensional spectral densities associated with three-time correlation functions, with the goal of studying non-Gaussian properties of the system.
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