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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Fokker-Planck equations for quantum amplifiers and squeezing

Alexander V. Gorokhov

Published May 9, 2001• 0 citations
Publisher

Abstract

The Fokker-Planck equations (FPE) which determine the time dependence of P -- symbol of the density matrix of quantum parametric amplifiers are derived and their group properties are investigated. Exploring the coherent states method, constructing the dynamical symmetry group of FPE and generalizing the well known Wei-Norman method to the case of FPE, we have found FPE solutions exactly. The initial squeezing influence of the thermal reservoir is discussed.

DOI
10.1117/12.426691

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A new method of elimination of squeezed field operators in nonlinear interaction with atomic subsystem is proposed. This method can be used for the opposite laser situation, in which the operators of an external coherent atomic source are eliminated from the density matrix equation. New types of master equations, belonging to su(1, 1) and su(2) symmetries are obtained. The solution of this equation is obtained using the generalized non-diagonal P and Q representations for su(1, 1) and su(2) symmetries. These master equations and their solutions can be used for further studies on the behavior of atomic polarization or quantum properties of the cavity field.