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Acta Physica Sinica

Wigner function of two-mode squeezed number state and its properties

Song Jun, Fan Hong‐Yi, Zhou Jun

Published Jan 1, 2011• 4 citations
Publisher

Abstract

By means of the entangled state representation as well as the Wigner operator in such a representation, the Wigner function of the two-mode squeezed number states is derived. The properties of corresponding Wigner function in the phase space are discussed by numerical calculation. The results indicate that Wigner function distribution in the phase space should be influenced by the correlation and the entanglement between two modes of two-mode squeezed number state.

DOI
10.7498/aps.60.110302

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By means of the entangled state representation as well as the Wigner operator in such a representation, the Wigner function of the two-mode squeezed number states is derived. The properties of corresponding Wigner function in the phase space are discussed by numerical calculation. The results indicate that Wigner function distribution in the phase space should be influenced by the correlation and the entanglement between two modes of two-mode squeezed number state.
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In this paper, two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and their normalization and completeness are investigated. Using the entangled state representation and Weyl ordering form of the Wigner operator, the Wigner functions of TDESVS are obtained and the variations of Wigner functions with the parameters m, n and r are investigated. Besides, two marginal distributions of Wigner functions of TDESVS are obtained, which exhibit some entangled properties of the two-particle's system in TDESVS.
By virtue of the squeezing-rotating entangled representation, we mainly establish the new two-mode phase operator and phase angle operator, which is a general form including the foregoing formalist in two-mode Fock space. In addition, the corresponding phase distribution function is given in the entangled representation. In terms of this definition, we also analyze the phase behavior of some simple two-mode states such as squeezing-rotating coherent state, squeezing-rotating vacuum state, and so on. It is found that the results exactly agree with the foregoing phase theory.
Based on the two-mode squeezing operator which is the quantum version of the symplectic transformation, we find that the corresponding squeezed two-mode number state is just a two-variable Hermite polynomial excited state, which possesses well-behaved features, e.g. its Wigner function is a direct product of two Laguerre polynomials; its Husimi function, a Gaussian broaden version of the Wigner function, is related to two-variable Hermite polynomials. Moreover, its quantum statistical features, such as squeezing properties and the inter-mode photon bunching, are discussed.