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Acta Physica Sinica

Boson inverse operators and associated even and odd coherent states

Qingyi Yang, Lian-Fu Wei, Ding Liang-En, (1)华东师范大学物理系，光谱学与波谱学教育部重点实验室，上海 200062; (2)华东师范大学物理系，光谱学与波谱学教育部重点实验室，上海 200062;广西大学物理系，南宁 530004; (3)上海交通大学物理系，上海 200030

Published Jan 1, 2003• 7 citations
Publisher

Abstract

A new kind of even and odd coherent states i.e.the photon-added and photon-deple ted states,can be obtained from acting boson inverse operators on the usual even and odd coherent states.The new states are the eigenstates of the operators a^ -ka^k+2 and a^+-ka2a^+k,r espectively.The results show that these states may reveal the anti-bunching and quantum squeezing effects.

DOI
10.7498/aps.52.1390

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•Nov 1, 2002•2 citations
A new kind of even and odd coherent states i.e.the photon-added and photon-deple ted states,can be obtained from acting boson inverse operators on the usual even and odd coherent states.The new states are the eigenstates of the operators a^ -ka^k+2 and a^+-ka2a^+k,r espectively.The results show that these states may reveal the anti-bunching and quantum squeezing effects.
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.
Making use of the recently introduced inverses of boson creation and annihilation operators, the authors show that the 'photon-added coherent states' are eigenstates of the operator (a Dagger m aa Dagger -m ) and also of the operator (a-ma Dagger -1 ) with eigenvalue alpha . The authors discuss completeness of these states. They obtain another family of photon-added coherent states which are proportional to a -m mod alpha ), where m is a positive integer and mod alpha ) is a coherent state. They show that these are the eigenstates of the operator (a -m a m+1 ) with eigenvalue alpha . Analogously, the authors introduce 'photon-depleted coherent states', a Dagger -m mod alpha ), and show that these are the eigenstates of the operator (a+ma Dagger -1 ) with eigenvalue alpha . The conditions for squeezing and antibunching of photons have also been discussed.
A new kind of nonlinear coherent states, i.e. the k eigenstates of the powers B^k (k ≥ 3) of the generalized annihilation operator B^=a^†-1f(N^) of f-oscillators, are constructed using the inverse operators of the boson annihilation and creation operators. The set of these states may form a complete quantum mechanics representation. Using newly defined higher order squeezing and an antibunching, the properties of the Mth-order squeezing and the antibunching effect of the k states are investigated. The results show that the Mth-order [M = (n + 1/2)k; n = 0, 1, 2, …] squeezing effects exist in all of the k states when k is even and the antibunching effect exists in all of the k states.
In this paper, we introduce a new family of photon-added as well as photon-depleted q -deformed coherent states related to the inverse q -boson operators. These states are constructed via the generalized inverse q -boson operator actions on a newly introduced family of q -deformed coherent states (Quesne C 2002 J. Phys. A: Math. Gen. 35 9213 ) which are defined by slightly modifying the maths-type q -deformed coherent states. The quantum statistical properties of these photon-added and photon-depleted states, such as quadrature squeezing and photon-counting statistics, are discussed analytically and numerically in the context of both conventional (nondeformed) and deformed quantum optics.
A new kind of even and odd nonlinear coherent states are defined. Using the numerical method, we have studied quantum statistical properties of the new even and odd nonlinear coherent states. It is shown that quantum statistical properties of the new even and odd nonlinear coherent states are very different from those of the usual even and odd coherent states. It is found that, in some ranges of 1beta1, the squeezing only exists in the new even nonlinear coherent state, and the amplitude-squared squeezing and antibunching effect appear for both new even and odd nonlinear coherent states.