Path integral quantization of the electromagnetic field in nonlinear dielectric materials

TL;DR

This paper develops a quantum field theory for light in nonlinear dielectric materials using path integral methods, capturing nonlinear responses like Kerr effects.

Contribution

It introduces a mesoscopic model incorporating fourth-order nonlinearity and derives Feynman rules for quantized fields in dispersive, absorptive media.

Findings

Constructed an effective action for nonlinear dielectric media.

Derived nonlinear response functions including Kerr nonlinearity.

Established Feynman rules for quantized electromagnetic fields in complex media.

Abstract

We construct a quantum theory of light in nonlinear dielectric media with dispersion and absorption. We employ a mesoscopic model for the light-matter interaction that include a fourth-order nonlinearity in the material response. Quantization is performed by constructing an effective action in a path-integral formalism by integrating out matter and bath degrees of freedom. We show how a nonlinear response function associated with Kerr nonlinearity is obtained through the model and, after full field quantization, we derive the Feynman rules from this theory.