A new finite-dimensional pair coherent state studied by virtue of the entangled state representation and its statistical behavior |
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Authors: | Xiang-Guo Meng Ji-Suo Wang Bao-Long Liang |
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Affiliation: | a Department of Physics, Liaocheng University, Liaocheng 252059, China b College of Physics and Engineering, Qufu Normal University, Qufu 273165, China |
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Abstract: | In this paper we construct a new type of finite-dimensional pair coherent states |ξ, q〉 as realizations of SU(2) Lie algebra. Using the technique of integration within an ordered product of operator, the nonorthogonality and completeness properties of the state |ξ, q〉 are investigated. Based on the Wigner operator in the entangled state |τ〉 representation, the Wigner function of |ξ, q〉 is obtained. The properties of |ξ, q〉 are discussed in terms of the negativity of its Wigner function. The tomogram of |ξ, q〉 is calculated with the aid of the Radon transform between the Wigner operator and the projection operator of the entangled state |η, κ1, κ2〉. In addition, using the entangled state |τ〉 representation of |ξ, q〉 to show that the states |ξ, q〉 are just a set of energy eigenstates of time-independent two coupled oscillators. |
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Keywords: | Finite-dimensional pair coherent state The technique of integration within an ordered product of operator Entangled state representation Statistical behavior |
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