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Journal of Optics B Quantum and Semiclassical Optics

Inverseq-boson operators and their relation to photon-added and photon-depleted states

L. F. Wei, Shun-Jin Wang, D. P. Xi

Published Sep 29, 1999• 8 citations
Publisher

Abstract

The generalized inverse of q -boson operators are introduced via their action on the q -number states. The q -analogy of photon-added and photon-depleted coherent states are constructed via the generalized inverse of q -boson operator actions on the q -coherent states. Their mathematical and quantum statistical properties are discussed in detail analytically and numerically.

DOI
10.1088/1464-4266/1/6/301

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Based on the coherent state (S1) and the operator [Formula: see text], we induce other three quantum states (here we abbreviate them as S2, S3 and S4). S2 is obtained by operating the operator on S1 directly. S3 is an orthogonal state of S1 constructed from the orthogonalizer relevant with that operator. S4 is a continuous-variable (CV) qubit state superposed from S1 and S3. We study and compare the mathematical and physical properties of such four quantum states. We demonstrate some statistical properties for S1–S4, including the mean photon number (MPN), anti-bunching effect, quadrate squeezing, photon number distribution, Husimi Q-function and Wigner function. The numerical results show some interesting non-classical characters for such states. It is worthy to note that the photon-added coherent state introduced by Agarwal and Tara is only a special case of our considered states.

Modern Physics Letters A•Sep 14, 2018•4 citations
The generalized inverse of q -boson operators are introduced via their action on the q -number states. The q -analogy of photon-added and photon-depleted coherent states are constructed via the generalized inverse of q -boson operator actions on the q -coherent states. Their mathematical and quantum statistical properties are discussed in detail analytically and numerically.
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.
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.
The photon-added nonlinear coherent states, defined as adaggerm∣alpha,f>{a}^{\\dagger m}|\\alpha, f>adaggerm∣alpha,f> up to a normalization constant, are still nonlinear coherent states with the nonlinear function f(N−m)[1−m/(N+1)]f(N-m)[1-m/(N+1)]f(N−m)[1−m/(N+1)]. Here % |\\alpha, f> is the nonlinear coherent state with the nonlinear function f(N)f(N)f(N), NNN is the number operator, adaggera^{\\dagger}adagger is the boson creation operator and mmm is a non-negative integer. We introduce a new type of nonlinear coherent states with the nonlinear function f(N+m)[1+m/(N+1)]f(N+m)[1+m/(N+1)]f(N+m)[1+m/(N+1)] obtained from the photon-added nonlinear coherent states with negative values of m.m.m. The nonlinear coherent states corresponding to the positive and negative values of mmm are shown to be the result of nonunitarily deforming the number states ∣m>|m>∣m> and ∣0>|0>∣0>, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of mmm in detail.
Based on the coherent state (S1) and the operator [Formula: see text], we induce other three quantum states (here we abbreviate them as S2, S3 and S4). S2 is obtained by operating the operator on S1 directly. S3 is an orthogonal state of S1 constructed from the orthogonalizer relevant with that operator. S4 is a continuous-variable (CV) qubit state superposed from S1 and S3. We study and compare the mathematical and physical properties of such four quantum states. We demonstrate some statistical properties for S1–S4, including the mean photon number (MPN), anti-bunching effect, quadrate squeezing, photon number distribution, Husimi Q-function and Wigner function. The numerical results show some interesting non-classical characters for such states. It is worthy to note that the photon-added coherent state introduced by Agarwal and Tara is only a special case of our considered states.