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International Journal of Modern Physics B

NONLINEAR SQUEEZED VACUUM STATES: NONCLASSICAL PROPERTIES

Mahmoud Darwish

Published Feb 10, 2005• 6 citations
Publisher

Abstract

Some of the properties of nonlinear squeezed vacuum states associated with trapped ions are considered, especially the photon number distribution, the phase properties, the Husimi–Kano Q function and the Wigner–Moyal W function of these nonlinear squeezed vacuum states. The structure of these functions is shown to depend on the nonlinearity parameter, its functional dependence and the squeezing parameter. It is shown that increasing the nonlinearity parameter results in the photon number distribution being squeezed independent.

DOI
10.1142/s0217979205026725

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Some of the properties of nonlinear squeezed vacuum states associated with trapped ions are considered, especially the photon number distribution, the phase properties, the Husimi–Kano Q function and the Wigner–Moyal W function of these nonlinear squeezed vacuum states. The structure of these functions is shown to depend on the nonlinearity parameter, its functional dependence and the squeezing parameter. It is shown that increasing the nonlinearity parameter results in the photon number distribution being squeezed independent.
We introduce a class of non-linear squeezed vacuum and one-photon states. Under conditions on the non-linearity function, these states are realizations of the SU (1,1) group. However, when a condition is removed, these states are defined as eigenstates of certain operators. Some of the properties of these states are investigated for the case of trapped ions. In particular, the Mandel q number, the photon number distribution, the phase properties, the Husimi–Kano Q -function and the Wigner–Moyal W -function of the non-linear squeezed one-photon states are discussed.
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In this paper, we introduce two new classes of nonlinear squeezed states that we name as f-deformed squeezed vacuum state |ξ, f〉 even and f-deformed squeezed first excited state |ξ, f〉 odd , which according to their production processes, essentially include only even and odd bases of Fock space, respectively. In the continuation, we introduce the superposition of these two distinct nonlinear squeezed states with a respective phase φ. Then, some of the criteria which imply the nonclassicality of the states, such as Mandel parameter, second-order correlation function, quadrature squeezing, amplitude-squared squeezing, Husimi and Wigner–Weyl quasi-distribution functions, are numerically examined. At last, by considering a well-known nonlinearity function associated with a nonlinear physical system, we present our results which outcome from the numerical calculations. It is shown that, the introduced f-deformed states can reveal high nonclassical features.
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.