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Journal of Physics A Mathematical and Theoretical

Entropy and entanglement dynamics in a quantum deformed coupled system

A N F Aleixo, A. B. Balantekin

Published Jul 2, 2008• 3 citations
Publisher

Abstract

A class of supersymmetric bound-state problems which represent the coupling of a two-level atom or molecule with a quantum-deformed shape-invariant potential system is introduced. We study the quantum dynamics of the partial entropies and the entanglement of the bipartite system as well as the excitation of the two-level atom for two possible forms of the pure initial state of the coupled system.

DOI
10.1088/1751-8113/41/31/315302

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A class of supersymmetric bound-state problems which represent the coupling of a two-level atom or molecule with a quantum-deformed shape-invariant potential system is introduced. We study the quantum dynamics of the partial entropies and the entanglement of the bipartite system as well as the excitation of the two-level atom for two possible forms of the pure initial state of the coupled system.
In this paper, within a parasupersymmetric and quantum deformed formalism, we introduce a class of bound-state problems which represents the coupling of a three-level atom with a two-dimensional potential system. We consider second-order parasupersymmetric quantum-mechanical models and a nonlinear deformed algebraic formulation for shape-invariant potential systems to study the quantum dynamics of physical observable, such as atomic level occupation, level transition probabilities, entropy and entanglement, in terms of time and deformation intensity. An application is given for a couple of shape-invariant potentials widely used to model quantum confined systems in several fields of physics, assuming a simple exponential form for the nonlinear deformation function.
A class of bound-state problems which represents the coupling of a three-level atom with a two-dimensional system involving two shape-invariant potentials was introduced in a previous paper. In this paper, we considered second-order parasupersymmetric quantum-mechanical models and two possible kinds for the coupling Hamiltonian (linear and nonlinear in the potential ladder operators). In the present paper, using an algebraic formulation for shape-invariant potential systems, we study the quantum dynamics of these coupled systems and obtain the temporal behaviour of some dynamical variables related with the atom and the coupling potentials. An application is given for a couple of shape-invariant potentials (Poschl–Teller + self-similar potentials).
The quantum dynamics of a two-level system coupled to a shape-invariant potential is investigated. Shape-invariant potentials share an integrability condition called shape invariance which identifies an underlying algebraic structure, in general infinite dimensional, that transforms the potential parameters such as strength, range and diffuseness. We determine the time-evolution operator, the density operator of the system, and obtain the temporal behaviour of various dynamical variables by considering either pure or mixed initial states of the system, constructed with the generalized coherent state of the shape-invariant coupling potential. We consider specific examples of shape-invariant coupling potentials (harmonic oscillator, Pöschl–Teller and self-similar potentials). The results obtained for all dynamical variables exhibit rapid oscillations which periodically collapse and regenerate in different ways depending on the coupling potential nature.