Exactly Solvable Models for Atom-Molecule Hamiltonians

Abstract

We present a family of exactly solvable generalizations of the Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or $\mathrm{S}\mathrm{U}(1,1)$ quasispins with a single boson field. They are obtained from the trigonometric Richardson-Gaudin models by replacing one of the SU(2) or $\mathrm{S}\mathrm{U}(1,1)$ degrees of freedom by an ideal boson. The application to a system of bosonic atoms and molecules is reported.