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Nonlinear optical signals from an assembly of N noninteracting particlesconsist of an incoherent and a coherent component, whose magnitudes scale \simN and \sim N(N-1), respectively. A unified microscopic description of bothtypes of signals is developed using a quantum electrodynamical (QED) treatmentof the optical fields. Closed nonequilibrium Green's function expressions arederived that incorporate both stimulated and spontaneous processes. General(n+1)-wave mixing experiments are discussed as an example of spontaneouslygenerated signals. When performed on a single particle, such signals cannot beexpressed in terms of the nth order polarization, as predicted by thesemiclassical theory. Stimulated processes are shown to be purely incoherent innature. Within the QED framework, heterodyne-detected wave mixing signals aresimply viewed as incoherent stimulated emission, whereas homodyne signals aregenerated by coherent spontaneous emission.

Nonlinear optical spectroscopy of single, few, and many molecules; nonequilibrium Green's function QED approach