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Acta Sinica Quantum Optica

The Wigner Function of One-mode Rotated and Squeezed State

HU Xiao-guang

Published Jan 1, 2008• 0 citations
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Abstract

In this paper,we propose a new kind of one-mode rotated and squeezed state,figure out its wigner function by virtue of the presented wigner operator,and further give the corresponding wigner marginal distribution.From the distribution,we can see that the marginal distribution of this squeezed state in coordinate or momentum space is the gaussian distribution.

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In this paper,we propose a new kind of one-mode rotated and squeezed state,figure out its wigner function by virtue of the presented wigner operator,and further give the corresponding wigner marginal distribution.From the distribution,we can see that the marginal distribution of this squeezed state in coordinate or momentum space is the gaussian distribution.
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.
We find that the exponential operator V ≡exp[ i λ( Q 1 P 2 + Q 2 P 3 +⋅⋅⋅+ Q n −1 P n + Q n P 1 )], Q i , P i are, respectively, the coordinate and momentum operators, is an n -mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V 's normally ordered expansion and obtain the n -mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.
A new formalism of the squeeze operator has been found by integration within normal ordered products. Based on this formalism, the essence of the formation of the squeezed state can be revealed directly and clearly. Various representations and properties of the squeezed state can be derived easily. It has been proved that the squeezed state is a coherent one in the quasiparticle space. The transformation relationship between squeezed states and eigenstates of both coordinate and momentum operators are presented. Also presented is the Wigner distribution function of the squeezed state.
We introduce the Wigner operator [Formula: see text] for the rotated quadrature phases and use the technique of integration within an ordered product of operators to derive its explicitly simpler form. Based on this, the mutual relations between [Formula: see text] and the corresponding marginal probability distribution operator can be easily revealed. The Wigner function theory is thus be recasted into a more elegant and concise formalism. The squeezing in rotated quadrature phase is discussed with the same method.