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Journal of Optics B Quantum and Semiclassical Optics

A class of nonlinear squeezed coherent states

A.‐S. F. Obada, G. M. Abd Al-Kader

Published Nov 22, 2005• 14 citations
Publisher

Abstract

Nonlinear extensions of the single-mode squeezed vacuum and squeezed coherent states are constructed. Nonlinear squeezed coherent states (NLSCSs) are defined and special cases of these states are discussed. Two cases of the definition are considered for the unitary and non-unitary deformation operator functions. Some nonclassical properties of these states are discussed. The Glauber second-order coherence function is calculated. Analytical and numerical results for the quadrature component distributions for the NLSCSs are presented. The s -parameterized quasi-probability function, especially the Wigner function, is discussed.

DOI
10.1088/1464-4266/7/12/028

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Nonlinear extensions of the single-mode squeezed vacuum and squeezed coherent states are constructed. Nonlinear squeezed coherent states (NLSCSs) are defined and special cases of these states are discussed. Two cases of the definition are considered for the unitary and non-unitary deformation operator functions. Some nonclassical properties of these states are discussed. The Glauber second-order coherence function is calculated. Analytical and numerical results for the quadrature component distributions for the NLSCSs are presented. The s -parameterized quasi-probability function, especially the Wigner function, is discussed.
The s-parameterized charactristic function for the superposition of squeezed coherent states (SCS's) is given. The s-parameterized distribution functions for the superposition of SCS's are investigated. Various moments are calculated by using this charactristic function. The Glauber second-order coherence function is calculated. The photon number distribution of the superposition of SCS's studied. Analytical and numerical results for the quadrature component distributions for the superposition of a pair of SCS's are presented. The phase distribution calculated from the integration of s-parameterized distribution function over the phase space. A generation scheme is discussed.
We have introduced the notion of ‘four-photon nonlinear coherent states’ (FPNCSs) as right eigenstates of the fourth power of the generalized annihilation operator A4. It has been shown that there are four possible sets of such states which all can be expressed as the deformed Schrödinger cat type states derived from the superposition of four nonlinear coherent states (NCSs) which are π/2 out of phase. The nonclassical properties of the FPNCSs would be studied for two well-known quantum systems, a Kerr-like medium and a trapped laser-driven ion far from the Lamb-Dicke regime. We have found that the depth or the domain of the nonclassical features of FPNCSs in terms of sub-Poissonian photon statistics, higher order squeezing as well as amplitude-squared squeezing are higher than the corresponding standard states. Specifically, the proposed states in this paper exhibit sub-Poissonian statistics over an extensive range of real amplitudes which is in contrast with the lower level of sub-Poissonian characteristics of four-photon standard coherent states. Also the depth or domain of the nonclassical features of the FPNCSs can be modified by changing the magnitude of the nonlinearity parameters. Analysis of the quasi-probability distributions like Glauber–Sudarshan P-function, Husimi Q-function and Wigner distribution function verifies the nonclassical nature of the presented states. Studying the cavity field evolution in the interaction of a single two-level atom with an even NCS in the framework of f-deformed Jaynes-Cummings model shows that such a system can potentially be considered as a possible source for generating the proposed states.