Supersymmetric and shape-invariant generalization for nonresonant and intensity-dependent Jaynes-Cummings systems

A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitr ary energy splittings between the two levels as well as intensity-dependent interactions. We show that the coupled-channel Hamiltonians obtained corre spond to the generalizations of the nonresonant and intensity-dependent Jay nes-Cummings Hamiltonians, widely used in quantized theories of lasers. In this general context, we determine the eigenstates, eigenvalues, the time e volution matrix and the population inversion matrix factor.