New Deformation of quantum oscillator algebra: Representation and some application

TL;DR

This paper introduces a new deformation of the quantum oscillator algebra with four parameters, providing explicit solutions for the energy spectrum, constructing deformed states, and analyzing their properties for quantum optics applications.

Contribution

It presents a novel four-parameter deformation of the oscillator algebra, including explicit energy spectrum solutions and analysis of deformed states and their commutators.

Findings

Explicit energy spectrum expressions derived.

Deformed states constructed and analyzed.

Correlation functions computed for quantum optics.

Abstract

This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic expressions of the energy spectrum are given. Deformed states are built and discussed with respect to the criteria of coherent state construction. Various commutators involving annihilation and creation operators and their combinatorics are computed and analyzed. Finally, the correlation functions of matrix elements of main normal and antinormal forms, pertinent for quantum optics analysis, are computed.