Barut-Girardello coherent states for nonlinear oscillator with position-dependent mass

TL;DR

This paper constructs and analyzes Barut-Girardello coherent states for a nonlinear oscillator with position-dependent mass, revealing their properties and how they reduce to classical oscillator results in the harmonic limit.

Contribution

It introduces a novel algebraic framework for nonlinear oscillators with variable mass and constructs associated coherent states using the Barut-Girardello formalism.

Findings

Coherent states exhibit specific statistical properties analyzed via Mandel parameter and correlation functions.

Results reduce to linear oscillator case in the harmonic limit.

Algebraic realization of SU(1,1) for the nonlinear oscillator is established.

Abstract

Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut-Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.