Systems with Intensity Dependent Conversion Integrable by Finite Orthogonal Polynomials

TL;DR

This paper provides exact solutions for models describing photon parametric down conversion, linking their Hamiltonians to finite orthogonal polynomials, and deriving spectra and eigenvectors.

Contribution

It introduces a novel class of exactly solvable models for photon conversion processes using finite orthogonal polynomials.

Findings

Spectra of the Hamiltonians are explicitly obtained.

Eigenvectors are explicitly constructed.

Models are exactly solvable using orthogonal polynomial techniques.

Abstract

We present exact solutions of a class of models, which describe the parametric down conversion of photons. The Hamiltonians of this models are related to the classes of finite orthogonal polynomials. The spectra and explicit expressions for eigenvectors of this Hamiltonians are obtained.