A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator

TL;DR

This paper constructs and analyzes nonlinear squeezed states of a generalized isotonic oscillator, exploring their non-classical properties, statistical behaviors, and phase-space distributions, revealing novel insights into their quantum features.

Contribution

It introduces the first detailed construction and analysis of nonlinear squeezed states for a generalized isotonic oscillator, including their statistical and non-classical properties.

Findings

Non-existence of dual nonlinear squeezed states in this system

Detailed characterization of Mandel's parameter and photon statistics

Derivation of the quasi-probability distribution function

Abstract

We construct nonlinear squeezed states of a generalized isotonic oscillator potential. We demonstrate the non-existence of dual counterpart of nonlinear squeezed states in this system. We investigate statistical properties exhibited by the squeezed states, in particular Mandel's parameter, second-order correlation function, photon number distributions and parameter $A_3$ in detail. We also examine the quadrature and amplitude-squared squeezing effects. Finally, we derive expression for the $s$-parameterized quasi-probability distribution function of these states. All these information about the system are new to the literature.