Quantum dynamics of a two-level system coupled to a shape-invariant potential

Abstract

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, Poschl–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.