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Journal of Liaocheng University

The Construction of Finite-dimensional Pair Coherent States and Its Characteristics Research

Fengming Zhang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

In this paper we construct a new type of finite-dimensional pair coherent states(FDPCS) and investigate their complete orthonormalized properties.Based on the Wigner operator in the entangled state representation,the Wigner function of is obtained.The nonclasscial properties of are discussed in terms of the negativity of its Wigner function.

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In this paper we construct a new type of finite-dimensional pair coherent states(FDPCS) and investigate their complete orthonormalized properties.Based on the Wigner operator in the entangled state representation,the Wigner function of is obtained.The nonclasscial properties of are discussed in terms of the negativity of its Wigner function.
This paper constructs a new type of finite-dimensional thermal coherent states (FDTCS), which differs from the proceeding thermal coherent state in construction, as realisations of SU(2) Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.
We theoretically analyze the photon number distribution, entanglement entropy, and Wigner phase-space distribution, considering the finite-dimensional pair coherent state (FDPCS) generated in the nonlinear Bose operator realization. Our results show that the photon number distribution is governed by the two-mode photon number sum q of the FDPCS, the entanglement of the FDPCS always increases quickly at first and then decreases slowly for any q, and the nonclassicality of the FDPCS for odd q is more stronger than that for even q.
In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states (EONLPCSs), which can be realized via operating the superposed evolution operators D±(τ) on the state |q, 0), is constructed, then their orthonormalized property, completeness relations and some nonclassical properties are discussed. It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations. Moreover, the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q,η and ζ.
The exponential form of even and odd pair coherent state (EOPCS) is constructed. The EOPCS is generalized to a finite dimensional EOPCS in the Hilbert space, and then its orthonormalized property, completeness relations and some noncalssical properties are discussed. It is shown that the finite dimensional EOPCS has normalized and completeness relations, but not orthogonal relations. By virtue of the numerical computation method, we find that, for any value of q, in different ranges of the parameter |ξ| the 5-dimensional EOPCS for the modes 1 and 2 exhibit anti-bunching effect and the photons between the two modes are always correlated. The different peak structures of the phase probability distributions for the 7-dimensional EOPCS show remarkably different quantum interference properties.
This paper introduces the generalized excited pair coherent state (GEPCS). Using the entangled state |η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q , α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state |η 1 , η 2 , τ 1 , τ 2 〉. The entangled states |η〉 and η 1 , η 2 , τ 1 , τ 2 〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.