Effects of magnetic sublevel degeneracy on Rabi oscillations

This paper describes the dynamics of multilevel excitation by coherent radiatin, in the $N$-level rotating-wave approximation, when the levels have nonzero angular momentum $J$ and consequent spatial-orientation degeneracy $2J+1$. Observable populations average over $2J+1$ independent sublevel excitation sequences. The phenomenon of inaccessible sublevels is noted, as is the effect of polarization. The paper illustrates how averaging over orientation can, in some cases, render illegible the Rabi oscillations and the ac Stark effect, whereas in other cases ($J\to J$, circular polarization on $J\to J\pm 1$ linear polarization) appreciable structure remains.