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 ($N=2J+1\mathrm{}$), 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.

• Received 13 March 1979

DOI:https://doi.org/10.1103/PhysRevA.20.539