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Chinese Physics B

Quasiprobability distributions of new kinds of even and odd nonlinear coherent states

Meng Xiang-Guo, Ji‐Suo Wang, Liang Bao-Long

Published Jun 1, 2009• 2 citations
Publisher

Abstract

Using a numerical computational method, quasiprobability distributions of new kinds of even and odd nonlinear coherent states (EONLCS) are investigated. The results show that the distributions of the new even nonlinear coherent states (NLCS) are distinct from those of the new odd NLCS and imply that the new EONLCS always exhibit some different nonclassical effects. Finally, with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics, the tomograms of the new EONLCS are calculated. This is a new way of obtaining the tomogram function.

DOI
10.1088/1674-1056/18/6/031

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Chinese Physics B•Feb 1, 2009•0 citations
Using a numerical computational method, quasiprobability distributions of new kinds of even and odd nonlinear coherent states (EONLCS) are investigated. The results show that the distributions of the new even nonlinear coherent states (NLCS) are distinct from those of the new odd NLCS and imply that the new EONLCS always exhibit some different nonclassical effects. Finally, with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics, the tomograms of the new EONLCS are calculated. This is a new way of obtaining the tomogram function.
A new kind of even and odd nonlinear coherent states (EONLCS) is constructed. Using the numerical computation method, the non-classical properties such as squeezing, amplitude-squared squeezing, anti-bunching and phase probability distribution of the new EONLCS are investigated. The results show that, in the different ranges of the parameter |λ|, the new EONLCS exhibits amplitude-squared squeezing in the directions Y1 and Y2. The squeezing effect is shown in the direction X2 for new even nonlinear coherent states, and the anti-bunching effect is shown for new odd nonlinear coherent states. Moreover, we find that the new EONLCS exhibit different quntum interference properties by studying the probability distributions of the states.
A new kind of even and odd nonlinear coherent states are defined. Using the numerical method, we have studied quantum statistical properties of the new even and odd nonlinear coherent states. It is shown that quantum statistical properties of the new even and odd nonlinear coherent states are very different from those of the usual even and odd coherent states. It is found that, in some ranges of 1beta1, the squeezing only exists in the new even nonlinear coherent state, and the amplitude-squared squeezing and antibunching effect appear for both new even and odd nonlinear coherent states.
Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, this paper derives the Wigner functions for the photon-depleted even and odd coherent states (PDEOCSs). Moreover, in terms of the Wigner functions with respect to the complex parameter α the nonclassical properties of the PDEOCSs are discussed. The results show that the nonclassicality for the state |β, m ⟩ o (or |β, m ⟩ e ) is more pronounced when m is even (or odd). According to the marginal distributions of the Wigner functions, the physical meaning of the Wigner functions is given. Further, the tomograms of the PDEOCSs are calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.