Two-level behavior of coherent excitation of multilevel systems

Previously published papers have noted the existence of two-level periodicities in idealized theoretical models of monochromatic excitation of multilevel systems. The present paper provides a theoretical derivation of such two-level dynamics from the more general N-level rotating-wave-approximation Schr\"odinger equation and applies the resulting formulas to different extremes of excitation in a nondegenerate system of sequential (ladderlike) excitation: first, when intermediate levels have much larger cumulative detunings than Rabi frequencies, and second, when intermediate Rabi frequencies are much larger than detunings. In each case one has simple analytic expressions for the effective two-level Rabi frequencies and detunings.