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Acta Physica Sinica

Some nonclassical properties of a finite dimensional even and odd pair coherent state

Meng Xiang-Guo, Ji‐Suo Wang, 聊城大学物理系,聊城 252059

Published Jan 1, 2007• 7 citations
Publisher

Abstract

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.

DOI
10.7498/aps.56.4578

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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.
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 photon-added odd pair coherent states and photon-added even pair coherent states are constructed,and their nonclassical properties are studied with numeric simulation method.The results show that the constructed states are new quantum optical fields that exhibit the nonclassical properties such as the sub-poissonian distribution characters of photon statistics and the antibunching effect.When the photons are added to the two modes of the odd(even) pair coherent states,the sub-poissonian distribution characters of photon statistics can be obviously enhanced.
The photon-subtracted odd(even) pair coherent states are constructed and their nonclassical properties are investigated by using numeric method.The results show that when the photons are subtracted from the first mode in the odd(even) pair coherent states,the sub-Poissonian distributing character of photon statistics of the second mode can be obviously enhanced.When the photons are subtracted from the first mode in the odd pair coherent states,the antibunching effect of the first mode will be enhanced as the modulus of the eigenvalue of the double modes photons annihilating operator is small.When the photons are subtracted from the first mode in the even pair coherent states,the antibunching effect of the second mode will be obviously enhanced as the modulus of the eigenvalue of the double modes photons annihilating operator is small.
The Roy-type even and odd nonlinear coherent states in a finite-dimensional Hilbert space are constructed. Their amplitude-squared squeezing effect, orthonormalized property, unitary property and completeness relations are discussed. The results reveal the existence of unitary property, completeness relations and non-orthonormalized property. There exists the amplitude-squared squeezing effect for the Roy-type even and odd nonlinear coherent states when the phase θ of parameter β meets the fixed condition. The relations between conditions of squeezing effect and parameters s,r and function f(n) are given. Finally using the numerical method, it is found that in some different ranges of r, the amplitude-squared squeezing effect exists in Roy-type even and odd nonlinear coherent states field in a finite-dimensional Hilbert space when the parameters s,θ and Lamb-Dike parameter η are given as the fixed value.