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Acta Physica Sinica

Displaced Excited Squeezed Vacuum States and Their Propertities

Sun Zhi-Hu, Fan Hong-Yi, 中国科学技术大学材料科学与工程系,合肥 230026

Published Jan 1, 2000• 5 citations
Publisher

Abstract

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.

DOI
10.7498/aps.49.74

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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.
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.
The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product (IWOP) of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state S'2(r) |00〉 are investigated. It is found that, in different ranges of the squeezed parameter r, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.
In this paper, we introduce two new classes of nonlinear squeezed states that we name as f-deformed squeezed vacuum state |ξ, f〉 even and f-deformed squeezed first excited state |ξ, f〉 odd , which according to their production processes, essentially include only even and odd bases of Fock space, respectively. In the continuation, we introduce the superposition of these two distinct nonlinear squeezed states with a respective phase φ. Then, some of the criteria which imply the nonclassicality of the states, such as Mandel parameter, second-order correlation function, quadrature squeezing, amplitude-squared squeezing, Husimi and Wigner–Weyl quasi-distribution functions, are numerically examined. At last, by considering a well-known nonlinearity function associated with a nonlinear physical system, we present our results which outcome from the numerical calculations. It is shown that, the introduced f-deformed states can reveal high nonclassical features.
Some of the properties of nonlinear squeezed vacuum states associated with trapped ions are considered, especially the photon number distribution, the phase properties, the Husimi–Kano Q function and the Wigner–Moyal W function of these nonlinear squeezed vacuum states. The structure of these functions is shown to depend on the nonlinearity parameter, its functional dependence and the squeezing parameter. It is shown that increasing the nonlinearity parameter results in the photon number distribution being squeezed independent.
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.