Quasiprobability distributions in dispersive optical bistability

K. Vogel and H. Risken
Phys. Rev. A 39, 4675 – Published 1 May 1989
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Abstract

For the model of Drummond and Walls [J. Phys. A 13, 725 (1980)] describing dispersive optical bistability, the s-parametrized quasidistributions W(α,s) introduced by Cahill and Glauber [Phys. Rev. A 117, 1882 (1969)] are investigated. The equation of motion for W(α,s) generally has derivative terms up to third order. For the Q function (s=-1) and the P function (s=1) the third-order terms vanish. The equation of motion is then a pseudo-Fokker-Planck equation, i.e., a Fokker-Planck equation where the diffusion matrix is not positive definite or semidefinite. It is shown that the equation of motion with the inclusion of third-order-derivative terms can be solved by the matrix continued-fraction method. In particular, results for the Wigner function (s=0) are presented and compared with the results of the Q function (s=-1). Furthermore, the results are compared also with those obtained from the equation of motion for the Wigner function where the third-order-derivative terms have been neglected.

  • Received 5 December 1988

DOI:https://doi.org/10.1103/PhysRevA.39.4675

©1989 American Physical Society

Authors & Affiliations

K. Vogel and H. Risken

  • Abteilung für Theoretische Physik, Universität Ulm, D-7900 Ulm, Federal Republic of Germany

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Vol. 39, Iss. 9 — May 1989

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