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Chinese Physics B

Finite-dimensional even and odd nonlinear pair coherent states and their some nonclassical properties

Meng Xiang-Guo, Ji‐Suo Wang, Tang-Kun Liu

Published Sep 1, 2008• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/17/9/034

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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.
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.
A new kind of even and odd nonlinear coherent states (EONLCS) is constructed. Using the numerical computation method, the non-classical properties such as squeezing, amplitude-squared squeezing, anti-bunching and phase probability distribution of the new EONLCS are investigated. The results show that, in the different ranges of the parameter |λ|, the new EONLCS exhibits amplitude-squared squeezing in the directions Y1 and Y2. The squeezing effect is shown in the direction X2 for new even nonlinear coherent states, and the anti-bunching effect is shown for new odd nonlinear coherent states. Moreover, we find that the new EONLCS exhibit different quntum interference properties by studying the probability distributions of the states.
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.
I theoretically construct a kind of new angular momentum coherent states by virtue of the nonlinear Bose SU(2) generators, and investigate their nonclassicality by analyzing the sub-Poissonian distributions, photon number distributions, entanglement entropy and Wigner phase-space distributions. The results show that the new states always have the sub-Poissonian distributions for all of the photon number sum [Formula: see text] of two modes, the photon number distributions are subjected to the parameter q, and the entanglement always increases quickly and then decreases slowly with increasing [Formula: see text], and the new states for odd q possess more stronger nonclassicality than for even q.