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Journal of Optics B Quantum and Semiclassical Optics

Statistical properties of nonlinear intermediate states: binomial state

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

Published Nov 22, 2005• 8 citations
Publisher

Abstract

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.

DOI
10.1088/1464-4266/7/12/036

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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.
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.
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We investigate the nonclassical properties of the single-mode binomial states of the quantized electromagnetic field. We concentrate our analysis on the fact that the binomial states interpolate between the coherent states and the number states, depending on the values of the parameters involved. We discuss their statistical properties, such as squeezing (second and fourth order) and sub-Poissonian character. We show how the transition between those two fundamentally different states occurs, employing quasiprobability distributions in phase space, and we provide, at the same time, an interesting picture for the origin of second-order quadrature squeezing. We also discuss the phase properties of the binomial states using the Hermitian-phase-operator formalism.
In this communication we investigate the action of a single-mode squeeze operator on the statistical behaviour of different binomial states. For the resulting states (squeezed generalized binomial states) normalized second-order correlation function, quasiprobability distribution functions and the distribution function P(x) associated with the quadrature x are studied both analytically and numerically. Furthermore, the quadrature phase distribution as well as the phase distribution in the framework of Pegg–Barnett formalism are discussed.