ALGEBRAIC STRUCTURE AND ANALYTIC SOLUTIONS OF GENERALIZED 3-LEVEL JAYNES-CUMMINGS MODELS

A generalized three-level Jaynes-Cummings model (JCM) which includes v arious ordinary JCMs is shown explicitly to have an SU(3) structure: t he Hamiltonian can be treated as a linear function of the generators o f the SU(3) group. Based on this algebraic structure, the exact algebr aic solutions of the Schrodinger equation, as well as eigenvalues and eigenstates of the Hamiltonian, are obtained by an algebraic method. T hus the three-level JCM is completely solved algebraically. The SU(N) structure of the N-level JCM is also constructed explicitly and can be solved by the same method.