Coherence vs incoherence in stepwise laser excitation

Abstract
We demonstrate the manner in which solutions of the (coherent) Schrödinger equation for multistep excitation approach those of an (incoherent) rate equation. For a two‐level system, coherence produces oscillations about the mean rate‐equation values. In more general N‐level sequences the two types of solutions agree in the limit described by Ackerhalt and Eberly. We point out instances in which a simple rate equation cannot duplicate results of the Schrödinger equation.