Quantum emitter interacting with a dispersive dielectric object: a model based on the modified Langevin noise formalism

TL;DR

This paper develops a comprehensive model for the interaction between a quantum emitter and a dispersive dielectric object using the modified Langevin noise formalism, revealing how the environment can be simplified to a single effective bath under certain conditions.

Contribution

It introduces a detailed quantum electrodynamics model that accounts for both medium-assisted and scattering-assisted fields without restrictions on the emitter's structure.

Findings

The electromagnetic environment can be represented by two baths or a single combined bath.

When initial bath states are thermal with the same temperature, the baths are equivalent.

The model provides conditions for simplifying the environment to a single effective bath.

Abstract

In this paper, we model the interaction of a quantum emitter with a finite-size dispersive dielectric object in an unbounded space within the framework of macroscopic quantum electrodynamics, using the modified Langevin noise formalism, without any restrictions on the emitter level structure or dipole operator. The quantized electromagnetic field consists of two contributions: the medium-assisted field, which accounts for the electromagnetic field generated by the noise polarization currents of the dielectric, and the scattering-assisted field, which takes into account the electromagnetic field incoming from infinity and scattered by the dielectric. We show that the emitter couples to two distinct bosonic baths: a medium-assisted bath and a scattering-assisted bath, each characterized by its own spectral density. We identify the conditions under which the electromagnetic environment composed of these two baths can be effectively replaced by a single bosonic bath, so that the reduced dynamics of the quantum emitter remain unchanged. In particular, when the initial states of the medium- and scattering-assisted baths are thermal states with the same temperature, we find that a single bosonic bath with a spectral density equal to the sum of the medium-assisted and scattering-assisted spectral densities is equivalent to the original electromagnetic environment.