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Chinese Physics B

Wigner functions and tomograms of the photon-depleted even and odd coherent states

Ji‐Suo Wang, Meng Xiang-Guo

Published Apr 1, 2008• 11 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/17/4/018

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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.
Using the coherent state representation of the Wigner operator, the Wigner function for the photon-added even and odd coherent state (PAEOCS) is obtained. In terms of the variations of the Wigner function with the complex parameter α in the phase space, the non-classical properties of the PAEOCS are discussed. It is found that the PAEOCS always exhibits the non-classical properties, and the photon-added even (or odd) coherent state exhibits the non-classical properties more easily when m is odd (or even). By virtue of the marginal distributions of the Wigner function for the PAEOCS, we illuminate the physical meaning of the Wigner function. Finally, based on the intermidate coordinate-momentum presentation the quantum tomogram function for the PAEOCS is obtained.
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.