Spectrum generating algebra of the C_{\lambda}-extended oscillator and multiphoton coherent states

TL;DR

This paper explores the algebraic structure of the $C_{inite}$-extended oscillator, constructs its coherent states, and analyzes their statistical and squeezing properties, unifying several known states as special cases.

Contribution

It introduces a polynomial deformation of su(1,1) algebra for the $C_{inite}$-extended oscillator and constructs its coherent states with detailed property analysis.

Findings

Coherent states include Barut-Girardello and $inite$-photon states as special cases

Detailed statistical and squeezing properties are characterized

The algebraic structure generalizes known oscillator models

Abstract

The $C_{\lambda}$-extended oscillator spectrum generating algebra is shown to be a $C_{\lambda}$-extended $(\lambda-1)$th-degree polynomial deformation of su(1,1). Its coherent states are constructed. Their statistical and squeezing properties are studied in detail. Such states include both some Barut-Girardello and the standard $\lambda$-photon coherent states as special cases.