Supersymmetric and Shape-Invariant Generalization for Nonresonant and Intensity-Dependent Jaynes-Cummings Systems

A class of shape-invariant bound-state problems which represent transition in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the couple-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent nonresonant Jaynes-Cummings Hamiltonians, widely used in quantized theories of laser. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.