Generalized Jaynes–Cummings Hamiltonians by shape-invariant hierarchies and their SUSY partners

Abstract

A generalization of the matrix Jaynes–Cummings model in the rotating wave approximation is proposed by means of the shape-invariant hierarchies of scalar factorized Hamiltonians. A class of Darboux transformations (sometimes called SUSY transformations in this context) suitable for these generalized Jaynes–Cummings models is constructed. Finally one example is worked out using the methods developed.