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Communications in Theoretical Physics

Some Properties of Two-mode Displaced Excited Squeezed Vacuum States

Meng Xiang-Guo, Ji‐Suo Wang, Liang Bao-Long

Published Sep 1, 2009• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/52/3/22

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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.
In this paper, the two-mode excited squeezed vacuum state (TESVS) is studied by using the statistical method. By calculating the normalization of the TESVS, a new form of Jacobi polynomials and some new identities are obtained. The photon number distribution of the TESVS is given and it is a simple form of Jacobi polynomials. Using the entangled state representation of Wigner operator, the Wigner function of the TESVS is obtainded and the variations of the Wigner function with the parameters m, n, and r are discussed. Here from the phase space point of view the TESVS can be well interpreted and described.
We introduce the states D(z)a\+\{+\+m\}S(r)|0〉 and examine their properties . Such states are checked to be complete vectors via the IWOP (Integration W ithin an Ordered Product of operators) technique. We find larger－scale macrosco pic oscillations of photon distribution after the squeezed vacuum states being e xcited and displaced. On contrary to the bunching photons of the squeezed vacuum states as the displacing parameter |z| and the excitation number m are both small photons coherence can exhibit antibunching effect. The quasi－proba bility distribution functions (Husimi Q( 醆+*) function and Wigner W(q p) function) are derived and their dependences on the three parameters (z m r) are discussed. The Wigner function obviously displays their nonclassical fe ature.
We investigate the statistical properties of the photon-subtractions from the two-mode squeezed vacuum state and its decoherence in a thermal environment. It is found that the state can be considered as a squeezed two-variable Hermite polynomial excitation vacuum and the normalization of this state is the Jacobi polynomial of the squeezing parameter. The compact expression for Wigner function (WF) is also derived analytically by using the Weyl ordered operators' invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of WF. The effect of decoherence on this state is then discussed by deriving the analytical time evolution results of WF. It is shown that the WF is always positive for any squeezing parameter and photon-subtraction number if the decay time exceeds an upper bound (}$κt>{1/2}\ln \frac{2\bar{n}+2}{2\bar{n}+1}).
Two-mode entangled-state wavefunctions and with complex variables z and y are introduced and investigated. They are direct analogues of the wavefunctions and in the single-mode case or are linearly related to each other by two-dimensional Fourier transformation. The states and are eigenstates of two pairs of commuting operators ( Z , Z † ) (or ( Q + , P − )) and ( Y , Y † ) (or ( P + , Q − )) to eigenvalues ( z , z * ) and ( y , y * ), respectively, and are normalized by means of the two-dimensional delta function. The entangled states and are represented as two limiting cases of two-mode squeezed coherent states. Different representations of these states, in particular, the analogue of the Agarwal–Simon representation of squeezed vacuum states, are derived and the properties of these states are discussed. The transition from the single-mode to the two-mode case is made using the common property of the squeezing operators to belong to different realizations of the abstract SU (1,1) group. The Wigner quasiprobability in representation of the states and is discussed and is explicitly calculated for two-mode squeezed vacuum (and squeezed coherent) states.