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Chinese Physics C

Antibunching Effect of k-Boson q-Coherent States

Zhong Wang

Published Jan 1, 2002• 0 citations
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Abstract

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.

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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.
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.
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.
We introduce a quantum antibunching effect. The quantum antibunching effect of the K eigenstates of the K th powere ( K greater than or equal to 3) of the annihilation operator in the Q-deformed non-harmonic oscillator is investigated. The physical meaning of the K states are explored. The results show that there is the quantum antibunching effect in all of those states. All of them can be generated by a linear superposition of generalized coherent states produced by the time-dependent Q-deformation non-harmonic oscillator at different instants.
The antibunching effect for the eigenstates of the k-th powers of the annihilation operator of two-parameter deformed harmonic oscillator (akqs,k≥3 ) is studied. Using the numerical method , we have studied the influences of the two parameter (qs ) deformation on the effect in the case of k = 3. It is shOwn that the eigenstates of akqs have anibunching effect when x = |α| 2,which reflects the intensity of the two-parameter deformed light field, is in values of certain intervals. The effect is evidently influeneed by the values of paratnters q and s.
A nonlinear theoretical model of interaction between q-deformed light field and a cascade three-level atom has been constructed. The formal solution of Schrodinger equation in the interactive representation and the expectation value of the interaction on such a state are obtained. Then, the influence of q deformation on photon antibunching effects is studied by numerical calculation. The results show that the more q deviates from 1, the stronger controllability to antibunching effects the q deformation has. It reflects the effect of the nonlinear behavior of q deformation on quantum coherence and quantum properties. When q→1, the theory reduces to the normal linear theory.
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.