Electromagnetic field quantization in a magnetodielectric medium with external charges

TL;DR

This paper presents a quantum model for electromagnetic fields in a magnetodielectric medium with external charges, deriving equations and analyzing spontaneous emission within a cavity environment.

Contribution

It introduces a novel quantum framework modeling the medium with two independent fields and derives related Maxwell and constitutive equations.

Findings

Derived Maxwell and constitutive equations from Heisenberg equations.

Calculated spontaneous emission rates considering medium susceptibilities.

Established a model linking quantum medium properties with cavity Green functions.

Abstract

The electromagnetic field inside a cubic cavity filled up with a linear magnetodielectric medium and in the presence of external charges is quantized by modelling the magnetodielectric medium with two independent quantum fields. Electric and magnetic polarization densities of the medium are defined in terms of the ladder operators of the medium and eigenmodes of the cavity. Maxwell and constitutive equations of the medium together with the equation of motion of the charged particles have been obtained from the Heisenberg equations using a minimal coupling scheme. Spontaneous emission of a two level atom embedded in a magnetodielectric medium is calculated in terms of electric and magnetic susceptibilities of the medium and the Green function of the cubic cavity as an application of the model.