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Journal of Modern Optics

Squeezed displaced fock states and non-diagonalPrepresentation

A.‐S. F. Obada, G. M. Abd Al-Kader

Published Apr 1, 1998• 11 citations
Publisher

Abstract

An R representation with a squeezed displaced-Fock-states (SDFSs) basis is introduced. A non-diagonal P representation for the density operator with SDFS basis is defined. The special cases for the fields, chaotic and laser, are calculated. The Pegg–Barnett phase distribution is given and compared with the radial integration of the generalized P function. The Fokker–Planck equation for the damped harmonic oscillator is considered, and its steady-state solution is given.

DOI
10.1080/09500349808230616

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•Jan 1, 2006•0 citations
An R representation with a squeezed displaced-Fock-states (SDFSs) basis is introduced. A non-diagonal P representation for the density operator with SDFS basis is defined. The special cases for the fields, chaotic and laser, are calculated. The Pegg–Barnett phase distribution is given and compared with the radial integration of the generalized P function. The Fokker–Planck equation for the damped harmonic oscillator is considered, and its steady-state solution is given.
The s-parametrized characteristic function for the superposition of squeezed displaced Fock states (SDFSs) is given. The s-parametrized distribution functions for the superposition of SDFSs are investigated. Various moments are calculated by using this characteristic function. The Glauber second-order coherence function is calculated. The squeezing properties of the superposition of SDFSs are studied. Analytical and numerical results for the quadrature component distributions for the superposition of a pair of SDFSs are presented. A generation scheme is discussed.
The Wigner quasi-probability function for the superposition of squeezed displaced Fock states (SDFS's) is reviewed. The interaction of these states with a two-level atom in cavity with the presence of additional Kerr medium is studied. Exact general matrix elements of the time-dependent operators of a Jaynes-Cummings model (JCM), in the presence of a Kerr medium, with these states are derived. We have obtained the phase distribution by two different ways: one is by Pegg-Barnett formalism, the second is by integration of the Wigner function over the radial variable. Results of these two approaches are compared. The Wigner phase distributions for some values of parameters are illustrated. The behaviors of the distributions have been shown as a function of the squeeze parameter in JCM.
The phase distribution obtained within the Pegg–Barnett Hermitian phase formalism is compared to the phase distributions obtained from the s -parametrized quasiprobability distributions integrated over the "radial" variable for some real states of the field. Exact analytical formulas for the s -parametrized phase distributions of coherent states, squeezed states, and displaced number states are obtained. A general formula relating the s -parametrized phase distributions to the Pegg–Barnett distribution is derived. Numerical examples illustrating the similarities and differences are presented in a graphical form.
The Wigner quasi-probability function for the superposition of squeezed displaced Fock states (SDFS’s) is reviewed. The interaction of these states with a two-level atom in cavity with the presence of additional Kerr medium is studied. Exact general matrix elements of the time-dependent operators of a Jaynes-Cummings model (JCM), in the presence of a Kerr medium, with these states are derived. We have obtained the phase distribution by two dierent ways: one is by Pegg-Barnett formalism, the second is by integration of the Wigner function over the radial variable. Results of these two approaches are compared. The Wigner phase distributions for some values of parameters are illustrated. The behaviors of the distributions have been shown as a function of the squeeze parameter in JCM.