Supersymmetric and Shape-Invariant Generalization for Non-resonant Jaynes-Cummings Systems

摘要

A class of shape-invariant bound-state problems which represent transitionsin a two-level system introduced earlier are generalized to include arbitraryenergy splittings between the two levels. We show that the coupled-channelHamiltonians obtained correspond to the generalization of the non-resonantJaynes-Cummings Hamiltonian, widely used in quantized theories of laser. Inthis general context, we determine the eigenstates, eigenvalues, the timeevolution matrix and the population inversion matrix factor.