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

TL;DR

This paper develops a quantum electrodynamical (QED) approach using nonequilibrium Green's functions to describe nonlinear optical signals from assemblies of molecules, revealing the nature of coherent and incoherent processes.

Contribution

It introduces a unified microscopic QED framework that captures both stimulated and spontaneous nonlinear optical signals, including for single molecules.

Findings

Coherent signals scale as N(N-1), incoherent as N.

Spontaneous signals cannot be expressed via polarization in single-molecule cases.

Heterodyne signals are incoherent stimulated emission; homodyne are coherent spontaneous emission.

Abstract

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