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Modern Physics Letters B

QUANTUM STATISTICAL PROPERTIES OF THE EVEN AND ODD NEGATIVE BINOMIAL STATES

Xiaoyan Zhang, Ji‐Suo Wang, Xiang‐Guo Meng, Jie Su

Published Aug 30, 2009• 1 citation
Publisher

Abstract

The properties of the even and odd negative binomial states are investigated. Mainly we concentrate on the statistical properties for such states and we consider the squeezing phenomenon by examining the variation in the quadrature variances. Using the Pegg–Barnett formalism of phase operator, the phase probability distributions of the states are discussed, and also the phase and number squeezing with different parameters are studied. The numerical computation results show that the phase probability distributions for the even and odd NBSs can clearly exhibit the different features of quantum effects.

DOI
10.1142/s0217984909020758

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The properties of the even and odd negative binomial states are investigated. Mainly we concentrate on the statistical properties for such states and we consider the squeezing phenomenon by examining the variation in the quadrature variances. Using the Pegg–Barnett formalism of phase operator, the phase probability distributions of the states are discussed, and also the phase and number squeezing with different parameters are studied. The numerical computation results show that the phase probability distributions for the even and odd NBSs can clearly exhibit the different features of quantum effects.
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.
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.
By using Wigner–Heisenberg algebra (WHA) and its Fock representation, even and odd Wigner negative binomial states (WNBSs) [Formula: see text] ([Formula: see text] corresponds to the ordinary even and odd negative binomial states (NBSs)) are introduced. These states can be reduced to the Wigner cat states in special limit. We establish the resolution of identity property for them through a positive definite measure on the unit disc. Some of their nonclassical properties, such as Mandel’s parameter and quadrature squeezing have been investigated numerically. We show that in contrast with the even NBSs, even WNBSs may exhibit sub-Poissonian statistics. Also squeezing in the field quadratures appears for both even and odd WNBSs. It is found that the deformation parameter [Formula: see text] plays an essential role in displaying highly nonclassical behaviors.