QED in dispersing and absorbing media

TL;DR

This paper develops a quantum electrodynamics framework for dispersing and absorbing media, extending classical Maxwell equations to quantum theory and analyzing interactions with atomic systems, including practical scenarios like spontaneous decay.

Contribution

It introduces a quantization scheme based on the microscopic Hopfield model, enabling quantum treatment of complex media and their interactions with atomic systems.

Findings

Derived input-output relations for absorbing devices

Analyzed spontaneous decay near absorbing surfaces

Extended quantization to amplifying and nonlinear media

Abstract

After giving an outline of the quantization scheme based on the microscopic Hopfield model of a dielectric bulk material, we show how the classical phenomenological Maxwell equations of the electromagnetic field in the presence of dielectric matter of given space- and frequency-dependent complex permittivity can be transferred to quantum theory. Including in the theory the interaction of the medium-assisted field with atomic systems, we present both the minimal-coupling Hamiltonian and the multipolar-coupling Hamiltonian in the Coulomb gauge. To illustrate the concept, we discuss the input--output relations of radiation and the transformation of radiation-field quantum states at absorbing four-port devices, and the spontaneous decay of an excited atom near the surface of an absorbing body and in a spherical micro-cavity with intrinsic material losses. Finally, we give an extension of the quantization scheme to other media such as amplifying media, magnetic media, and nonlinear media.