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Acta Physica Sinica

Wigner function of a kind of special single-mode squeezed state

YU Hai-jun, Jian-ming Du, Xiulan Zhang

Published Jan 1, 2011• 0 citations
Publisher

Abstract

In this paper, the expression of Wigner operator in the coherent state is derived using the IWOP technology. The Wigner function of a kind of special single-mode squeezed state is calculated. When the rotation parameter value changes, the numerical calculations show that the Wigner function in the phase space possesses a rotation displacement feature.

DOI
10.7498/aps.60.090305

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In this paper, the expression of Wigner operator in the coherent state is derived using the IWOP technology. The Wigner function of a kind of special single-mode squeezed state is calculated. When the rotation parameter value changes, the numerical calculations show that the Wigner function in the phase space possesses a rotation displacement feature.
We find a new κ-parameter squeezed coherent state | p , q ⟩ κ representation, which possesses well-behaved features, i.e., its Wigner function's marginal distribution in the `` q -direction'' and in the `` p -direction'' is the Gaussian form exp {−κ( q '− q ) 2 }, and exp {( p '− p ) 2 /κ}, respectively. Based on this, the Husimi function of | p , q ⟩ κ is also obtained, which is a Gaussian broaden version of the Wigner function. The | p , q ⟩ κ state provides a good representative space for studying various properties of the Husimi operator.
One- and two-mode successively squeezed state, obtained through re-squeezing two single mode squeezed states by the two-mode squeezing operator, is studied in terms of the technique of integration within an ordered product (IWOP) of operators. We first derive the normally ordered form of this one- and two-mode successively squeezing operator, and then investigate the quantum statistical properties of the corresponding squeezed state. Particularly, we use the Weyl ordering invariance under a similar transformation to derive the analytical expression of its Wigner function, which seems very easy and concise. Finally, the experimental generation of one- and two-mode successively squeezed state is also proposed simply.
Abstract Coherent states, in Wigner representation of quantum mechanics which is classical in structure with Wigner function playing the role of classical phase space probability distribution, and standard quantum mechanical expression for average values of corresponding Weyl quantum operators, general expression for matrix elements of the operator corresponding to phase of the oscillator by Weyl procedure, are obtained in the |n〉 basis. The general expression for matrix elements in the same basis of any other operator is also obtained. As the only mathematical technique necessary in the proposed procedure is a simple change of variables to polar coordinates in the corresponding integrals, this way to introduce Weyl phase operator, and some other operators in Weyl quantization, greatly simplifies necessary derivations and calculations.