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Chinese Physics C

Pair q-Coherent States and Their Antibunching Effects

Zhongqing Wang, Li Junhong, AN Guang-lei

Published Jan 1, 2005• 0 citations
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Abstract

Using the properties of the q-deformed boson creation and annihilation operators and their inversed operators, two kind of q-deformed pair coherent states are introduced. Antibunching effects and correlation properties between two modes in the states are investigated. It is shown that q-deformed pair coherent states exhibit antibunching effects and the photons of the two modes are correlated. These nonclassical effects are influenced by the parameter q. These effects increase when ｜lnq｜ increases.

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Using the properties of the q-deformed boson creation and annihilation operators and their inversed operators, two kind of q-deformed pair coherent states are introduced. Antibunching effects and correlation properties between two modes in the states are investigated. It is shown that q-deformed pair coherent states exhibit antibunching effects and the photons of the two modes are correlated. These nonclassical effects are influenced by the parameter q. These effects increase when ｜lnq｜ increases.
The antibunching effect for the eigenstates of the q deformed annihilation operator a k q(k ≥3) is investigated. Using the numerical method, we have studied the influences of the q parameter deformation on the effect in the case of k =3. The results show that the eigenstates of a k q exhibit antibunching effect when x=|z| 2, i.e. the intensity of the oscillator in q deformed coherent state, is in values of certain intervals, and the effect is evidently influenced by the values of parameter q . When the intensity of the q deformed light field is changed stronger gradually, the fluctuation of the photon number in the light field is changed between the classical (or quantum) and the quantum (or classical) properties alternatively.
This paper defines the Mandel Q-parameter of the q-deformed coherent state,and deduces the relation between the q-deformed Mandel Q-parameter and the q-deformed second-order correlation function.It proves that both the sub-Poissonian character and the antibunching effect in the q-deformed coherent state are not equivalent.The sub-Poissonian character of the photon-added k-boson q-coherent state is numerically studied.The result indicates that the sub-Poissonian character is evidently dependent on increased number m of photons.
The generalized inverses of q -boson operators denoted by are introduced via their acting on the q -number states. The even and odd number eigenstates of two photon operators are constructed. It is shown that these states can show quantum-squeezing. However, their even number states always show quantum-antibunching, while their odd number states always show quantum-bunching. This result is different from that in recent paper (C.L. Mehta, A.K. Roy and G.M. Saxena, Phys. Rev. A46 (1992) 1565) where the odd number eigenstates of operators with q ≡ 1 show bunching for some parameter values and antibunching for other parameter values.
The antibunching properties for the eigenstates of the Kth powers (K≥3) of the annihilation operator of the q-deformed non-harmonic oscillator are investigated. The numerical method is used to study the properties influenced by the parameter q. The results show that the eigenstates exhibit antibunching effects in a number of intervals of x=β2, which reflects the intensity of the non-harmonic oscillator in q-deformation generalized coherent state. The effects are evidently influenced by the parameter q. When q is taken values departure from 1 greatly, these intervals become larger, and shift toward the positive x direction.
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.
Two-mode charge (pair) coherent states have been introduced previously by using the 〈η| representation. In this paper, we reobtain these states by a rather different method. Then, using the nonlinear coherent state approach and based on a simple manner by which the representation of two-mode charge coherent states is introduced, we generalize the bosonic creation and annihilation operators to the f -deformed ladder operators and construct a new class of f -deformed charge coherent states. Unlike the (linear) pair coherent states, our presented structure has the potential to generate a large class of pair coherent states with various nonclassicality signs and physical properties which are of interest. For this purpose, we use a few well-known nonlinearity functions associated with particular quantum systems as some physical appearances of our presented formalism. After introducing the explicit form of the above correlated states in the two-mode Fock space, several nonclassicality features of the corresponding states (as well as the two-mode linear charge coherent states) are numerically investigated by calculating quadrature squeezing, the Mandel parameter, the second-order correlation function, the second-order correlation function between the two modes and the Cauchy–Schwartz inequality. Also, the oscillatory behaviour of the photon count and the quasi-probability (Husimi) function of the associated states will be discussed. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.