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Journal of Mathematical Physics

Purely squeezed states for quantum deformed systems

A N F Aleixo, A. B. Balantekin

Published Jun 1, 2008• 5 citations
Publisher

Abstract

The generalized purely squeezed states for primary shape-invariant potentials systems, quantum deformed by different models, are constructed by the ladder-operator method within an algebraic approach based on supersymmetric quantum mechanics. The characteristic properties of these states as well as their quantum statistical properties and squeezing effects for generalized quadrature observables are studied and analyzed in terms of the quantum deformation parameter q. An application is given for a quantum deformed Pöschl–Teller potential system, and numerical results are presented and discussed in detail.

DOI
10.1063/1.2939392

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The generalized purely squeezed states for primary shape-invariant potentials systems, quantum deformed by different models, are constructed by the ladder-operator method within an algebraic approach based on supersymmetric quantum mechanics. The characteristic properties of these states as well as their quantum statistical properties and squeezing effects for generalized quadrature observables are studied and analyzed in terms of the quantum deformation parameter q. An application is given for a quantum deformed Pöschl–Teller potential system, and numerical results are presented and discussed in detail.
Generalized coherent states for primary shape invariant potential systems quantum deformed by different models are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show that this generalized formalism is able (a) to supply the essential requirements necessary to establish a connection between classical and quantum formulations of a given system, (b) to reproduce, as particular cases, results already known for shape-invariant systems (such as standard harmonic oscillator and Pöschl–Teller potentials as well as quantum deformed harmonic oscillator models) and (c) point to a formalism that provides a unified description of the different kind of coherent states for quantum systems, deformed or not deformed.
We obtain the Robertson–Schrödinger uncertainty relation for shape-invariant systems and construct generalized Robertson intelligent states for these systems using an algebraic approach based on the supersymmetric quantum mechanics. Using the variances of generalized quadrature operators we study the coherency and squeezing properties, evaluating their dependence on different kinds of generalizations for shape-invariant systems with potential parameters related by a translation (Pöschl–Teller potential) and by a scaling (self-similar potential).
Using an algebraic approach, we construct purely coherent and squeezed states for a set of exactly solvable quantum confined systems assuming a generalization of both the ladder-operator and the displacement-operator methods, showing the equivalence between the two procedures. We obtain the analogue of the displacement and the squeeze operators and study their basic relations and their connections with the properties of the purely coherent and squeezed states that they produce. In a second approach, we construct generalized squeezed coherent and intelligent states for these systems considering the successive action of the displacement and the squeeze operators (in the first case) and the combined action of these operators (in the second case). We apply the generalized approach for shape-invariant systems with potential parameters related by a translation and by a scaling and show that the presence of the generalizing functionals of the potential parameters in the formalism opens a large number of possibilities in the construction of these special quantum states.
Abstract We construct a generalized version of the photon-subtracted squeezed vacuum states (PSSVS), which can be utilized to construct the same for nonlinear, deformed and any usual quantum mechanical models beyond the harmonic oscillator. We apply our general framework to trigonometric Pöschl–Teller potential and show that our method works accurately and produces a proper nonclassical state. We analyze the nonclassicality of the state using three different approaches, namely, quadrature squeezing, photon number squeezing and Wigner function and indicate how the standard definitions of those three techniques can be generalized and utilized to examine the nonclassicality of any generalized quantum optical states including the PSSVS. We observe that the generalized PSSVS are always more nonclassical than those arising from the harmonic oscillator. Moreover, within some quantification schemes, we find that the nonclassicality of the PSSVS increases almost proportionally with the number of photons subtracted from the generalized squeezed vacuum state. Thus, generalized PSSVS may provide an additional freedom with which one can regulate the nonclassicality and obtain an appropriate nonclassical state as per requirement.