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Acta Physica Sinica

Wigner function for the photon-added even and odd coherent state

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

Published Jan 1, 2007• 12 citations
Publisher

Abstract

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.

DOI
10.7498/aps.56.2160

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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 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.
We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a 2. We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.
Wigner functions in phase space are reconstructed for the excited coherent states，which are generated by applying the inverse of k-Boson operators repeatedly to the coherent states. The non-classicality of these states is discussed by calculating their Wigner functions in Fock-state space. Numerical results show that these excited coherent states always reveal non-classical characteristics，no matter whether the excited number k is even or odd，and also the corresponding non-classicality is more obvious with the number k increasing.
Based on the expressions of Wigner functions in Fock-spaces,we reconstruct the Wigner functions of photon-added and-subtracted states of squeezed vacuum states.Negativities of these Wigner functions numerically indicate that these states are really non-classical quantum states.We also discuss how these negativities depend on the photon number k added to and subtraced from the squeezed vacuum states.The negativities are greater when k is odd numbers than those when k is even numbers.The result provides a theoretical foundation for measuring these states.