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Acta Physica Sinica

New even and odd nonlinear coherent states and their non-classical properties

Meng Xiang-Guo, Ji‐Suo Wang, 聊城大学物理系,聊城 252059

Published Jan 1, 2007• 4 citations
Publisher

Abstract

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.

DOI
10.7498/aps.56.2154

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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 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.
We construct a class of nonlinear coherent states (NLCSs) by introducing a more general nonlinear function and study their nonclassical properties, specifically the second-order correlation function [Formula: see text], Mandel parameter Q, squeezing, amplitude-squared squeezing and Wigner function of the optical field. The results indicate that the nonclassical properties of the new types of even and odd NLCSs crucially depend on the nonlinear functions. More concretely, we find that the new even NLCSs could exhibit the photon-bunching effect, whereas the new odd NLCSs could show the photon-antibunching effect. The degree of squeezing is also significantly affected by the parameter selection of these NLCSs. By employing various forms of nonlinear functions, it becomes possible to construct the NLCSs with diverse properties, thereby providing a theoretical foundation for the corresponding experimental investigations.
The spueezing properties in a new kind of even and odd nonlinear coherent states are discussed via the measurement phase operators introduced by Barnett S M and Pegg D T. It is found that there are only a kind of CS squeezing but there are not CN and SN squeezing. Using the numerical calculation, we studied the squeezing properties of CS. It is shown that the CS squeezing properties of the even and odd nonlinear coherent states are different from those of usual even and odd coherent states. Squeezing exists for the new even nonlinear coherent states in the wide range, while small range for the new odd nonlinear coherent states.