Reduction of degenerate two-level excitation to independent two-state systems

Examining the dynamics of a degenerate two-level system excited by coherent resonant light, we exhibit a transformation of basis states which reduces the problem to a set of independent nondegenerate one- and two-state systems. More generally, reduction of multilevel Hamiltonians requires only that the states can be collected into two sets; within each set the states are degenerate, unlinked by Hamiltonian matrix elements. The remaining Hamiltonian linkages must share the same time dependence, but are otherwise arbitrary. We apply this method to reduction of the angular momentum degeneracy of a two-level atom excited by elliptically polarized light and to multiple-laser resonant excitation of multiple levels into a common level