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International Journal of Geometric Methods in Modern Physics

Nonlinear time evolution of coherent states with observation of super revivals in a generalized isotonic oscillator

V. Chithiika Ruby, Paulsamy Muruganandam, Murugaian Senthilvelan

Published Nov 29, 2013• 0 citations
Publisher

Abstract

In this paper, we investigate revival and super revivals of nonlinear coherent states while generating these states through the interaction of coherent states of a generalized isotonic oscillator with the nonlinear media during time evolution. We construct the f-deformed generalized isotonic oscillator which is a non-isochronous partner of the generalized isotonic oscillator. We connect these two nonlinear oscillators through deformed ladder operators. The generalized isotonic oscillator possesses linear energy spectrum whereas f-deformed generalized isotonic oscillator exhibits nonlinear energy spectrum. The presence of the cubic nonlinearity in the f-deformed oscillator motivates us to study revivals, super and fractional revivals of coherent states which are nonlinearly evolved. We also investigate time-dependent expectation values of uncertainties in certain canonically conjugate variables and demonstrate that at revival and super revival times the uncertainty relation attains its minimum value.

DOI
10.1142/s0219887814500273

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We construct nonlinear coherent states or f -deformed coherent states for a nonpolynomial nonlinear oscillator which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (Cariñena et al 2008 J. Phys. A: Math. Theor. 41 085301 ). The deformed annihilation and creation operators which are required to construct the nonlinear coherent states in the number basis are obtained from the solution of the Schrödinger equation. Using these operators, we construct generalized intelligent states, nonlinear coherent states, Gazeau–Klauder coherent states and the even and odd nonlinear coherent states for this newly solvable system. We also report certain nonclassical properties exhibited by these nonlinear coherent states. In addition to the above, we consider the position-dependent mass Schrödinger equation associated with this solvable nonlinear oscillator and construct nonlinear coherent states, Gazeau–Klauder coherent states and the even and odd nonlinear coherent states for it. We also give explicit expressions of all these nonlinear coherent states by considering a mass profile which is often used for studying transport properties in semiconductors.
Abstract We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau–Klauder formalism and discuss some of their properties. In order to investigate the temporal evolution we first explore the statistical properties by means of weighting distribution and the Mandel parameter. It is found that the temporal evolution of the coherent states may exhibit the phenomena of quantum revivals and fractional revivals for a particular choice of position-dependent mass oscillator.
We consider the time-dependent bi-coherent states that are essentially the Gazeau-Klauder coherent states for the two dimensional noncommutative harmonic oscillator. Starting from some q-deformations of the oscillator algebra for which the entire deformed Fock space can be constructed explicitly, we define the q-deformed bi-coherent states. We verify the generalized Heisenberg’s uncertainty relations projected onto these states. For the initial value in time, the states are shown to satisfy a generalized version of Heisenberg’s uncertainty relations. For the initial value in time and for the parameter of noncommutativity θ = 0, the inequalities are saturated for the simultaneous measurement of the position-momentum observables. When the time evolves, the uncertainty products are different from their values at the initial time and do not always respect the generalized uncertainty relations.