Exactly-solvable models for atom-molecule hamiltonians

TL;DR

This paper introduces a family of exactly-solvable models extending the Jaynes-Cummings framework, describing interactions between quasi-spin ensembles and a boson field, with applications to atom-molecule systems.

Contribution

It develops new exactly-solvable models for atom-molecule interactions by generalizing Richardson-Gaudin models with bosonic degrees of freedom.

Findings

Models are exactly solvable using algebraic methods.

Application demonstrated for bosonic atom and molecule systems.

Provides analytical solutions for complex quantum interactions.

Abstract

We present a family of exactly-solvable generalizations of the Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or SU(1,1) quasi-spins with a single boson field. They are obtained from the trigonometric Richardson-Gaudin models by replacing one of the SU(2) or SU(1,1) degrees of freedom by an ideal boson. Application to a system of bosonic atoms and molecules is reported.