Ladder operators and squeezed coherent states of a 3-dimensional generalized isotonic nonlinear oscillator

TL;DR

This paper constructs and analyzes three-dimensional squeezed coherent states of a generalized isotonic oscillator, demonstrating their nonclassical properties, photon statistics, and phase space squeezing through analytical methods.

Contribution

It introduces a complete set of three-mode squeezed coherent states for a new generalized isotonic oscillator using $X_1$-Laguerre polynomials, including their nonclassical features.

Findings

States exhibit sub-Poissonian and super-Poissonian photon statistics

States demonstrate squeezing in radial and angular parts

Wigner functions confirm nonclassical squeezing properties

Abstract

We explore squeezed coherent states of a 3-dimensional generalized isotonic oscillator whose radial part is the newly introduced generalized isotonic oscillator whose bound state solutions have been shown to admit the recently discovered $X_1$-Laguerre polynomials. We construct a complete set of squeezed coherent states of this oscillator by exploring the squeezed coherent states of the radial part and combining the latter with the squeezed coherent states of the angular part. We also prove that the three mode squeezed coherent states resolve the identity operator. We evaluate Mandel's $Q$-parameter of the obtained states and demonstrate that these states exhibit sub-Possionian and super-Possionian photon statistics. Further, we illustrate the squeezing properties of these states, both in the radial and angular parts, by choosing appropriate observables in the respective parts. We also evaluate Wigner function of these three mode squeezed coherent states and demonstrate squeezing property explicitly.