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Physica Scripta

Nonclassical properties of a nonlinear generalized geometric state

M. Sebawe Abdalla, A.‐S. F. Obada, Mahmoud Darwish

Published Apr 23, 2008• 2 citations
Publisher

Abstract

In this paper, we introduce and investigate some properties of a nonlinear generalized geometric state (the state that interpolates between the number state and a nonlinear pure thermal state). We mainly concentrate on the statistical properties. We have discussed the normal squeezing as well as the amplitude squared squeezing, further the Mandel's q-parameter is also considered. The investigation is also extended to include the quasi-probability distribution functions (W-Wigner and Q-functions). The quadrature distribution and the phase properties in the Pegg–Barnett formalism besides the phase variances are considered.

DOI
10.1088/0031-8949/77/05/055002

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In this paper, we introduce and investigate some properties of a nonlinear generalized geometric state (the state that interpolates between the number state and a nonlinear pure thermal state). We mainly concentrate on the statistical properties. We have discussed the normal squeezing as well as the amplitude squared squeezing, further the Mandel's q-parameter is also considered. The investigation is also extended to include the quasi-probability distribution functions (W-Wigner and Q-functions). The quadrature distribution and the phase properties in the Pegg–Barnett formalism besides the phase variances are considered.
In the present paper we introduce a nonlinear binomial state (the state which interpolates between the nonlinear coherent and number states). The main investigation concentrates on the statistical properties for such a state where we consider the squeezing phenomenon by examining the variation in the quadrature variances for both normal and amplitude-squared squeezing. Examinations for the quasi-probability distribution functions ( W -Wigner and Q -functions) are also given for both diagonal and off diagonal terms. The quadrature distribution and the phase distribution as well as the phase variances are discussed. Moreover, we give in detail a generation scheme for such state.
The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg—Barnett formalism. Then, two nonclassical features, i.e., squeezing in the number and phase operators, as well as the number—phase Wigner function of the generalized squeezed states are investigated. Due to some actual physical situations, the present approach is applied to two classes of generalized squeezed states: solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions. Finally, the time evolution of the nonclassical properties of the considered systems has been numerically investigated.
We construct nonlinear squeezed states of a generalized isotonic oscillator potential. We demonstrate the non-existence of a dual counterpart of nonlinear squeezed states in this system. We investigate the statistical properties exhibited by the squeezed states, in particular Mandel's parameter, second-order correlation function, photon number distributions and parameter A 3 in detail. We also examine the quadrature and amplitude-squared squeezing effects. Finally, we derive the expression for the s -parameterized quasi-probability distribution function of these states. All this information about the system is new to the literature.
New states of electromagnetic field, generalized excited negative binomial states are introduced here. These states interpolate between the superposition of two excited coherent states and number states. The non-classical properties for these states are discussed, such as, second order correlation function, squeezing phenomena [normal squeezing and amplitude squared squeezing], phase properties in Pegg–Barnett formalism and the quasi-probability distribution functions (Q-function and Wigner function).