Supersymmetric Quantum Mechanics, multiphoton algebras and coherent states

TL;DR

This paper explores multiphoton algebras and coherent states in supersymmetric quantum mechanics, revealing polynomial deformations of single-photon algebras and analyzing their properties and uncertainty relations.

Contribution

It introduces polynomial deformations of multiphoton algebras for SUSY partner Hamiltonians and constructs associated Barut-Girardello coherent states.

Findings

Multiphoton algebras are polynomial deformations of single-photon algebras.

Barut-Girardello coherent states are explicitly constructed.

Uncertainty relations for these states are analyzed.

Abstract

The multiphoton algebras for one-dimensional Hamiltonians with infinite discrete spectrum, and for their associated kth-order SUSY partners are studied. In both cases, such an algebra is generated by the multiphoton annihilation and creation operators, as well as by Hamiltonians which are functions of an appropriate number operator. The algebras obtained turn out to be polynomial deformations of the corresponding single-photon algebra previously studied. The Barut-Girardello coherent states, which are eigenstates of the annihilation operator, are obtained and their uncertainty relations are explored by means of the associated quadratures.