By employing an analogy with a spin-
J system in a constant magnetic field the authors obtain a simple soluble model for stepwise laser excitation of an
N-level system (
N=2J+1), including analytic treatment of Doppler detuning and of ionization loss. The solutions are periodic and hence permit complete population inversion. A simple graphical realization of the population dynamics, a generalization of the Feynman, Vernon, and Hellwarth vector model of the two-level Bloch equation, is then described.
We derive the analytical solution of the model of a two-state system interacting with an external coherent field, in which the Hamiltonian is pseudo-Hermitian. We describe in detail the non-Hermitian generalization of the famed Landau-Zener-St\"uckelberg-Majorana model, but similar generalizations can be derived in a very simple fashion for the other analytically soluble two-state models. The analytical solutions possess a non-Hermitian dynamical invariant, which replaces the probability conservation condition in the Hermitian case. Implementations in waveguide optics and nonlinear frequency conversion are suggested.