Quantum statistical properties of some new classes of intelligent states associated with special quantum systems

TL;DR

This paper introduces a new algebraic formalism for constructing intelligent states in quantum systems, demonstrating its application to various physical models and analyzing their nonclassical properties through statistical measures.

Contribution

A novel formalism for f-deformed intelligent states applicable to systems with known spectra and nonlinearity functions is proposed and demonstrated.

Findings

New classes of intelligent states for trapped ions, harmonious states, and hydrogen-like spectra are constructed.

The nonclassical properties of these states are analyzed using Mandel parameter and quadrature squeezing.

Numerical results confirm the nonclassical features of the introduced states.

Abstract

Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems with a known discrete spectrum as well as the generalized coherent states with known nonlinearity function $f (n)$. As some physical appearance of the proposed formalism, a few new classes of intelligent states associated with \textit{`center of-mass motion of a trapped ion'}, \textit{`harmonious states'} and \textit{`hydrogen-like spectrum'} have been realized. Finally, the nonclassicality of the obtained states has been investigated. To achieve this purpose the quantum statistical properties using the Mandel parameter and the squeezing of the quadratures of the radiation field corresponding to the introduced states have been established numerically.