System-environment coupling derived by Maxwell's boundary conditions from weak to ultrastrong light-matter coupling regime

TL;DR

This paper derives a fundamental description of system-environment coupling in cavity QED across weak to ultrastrong regimes using Maxwell's boundary conditions, emphasizing polariton conservation.

Contribution

It introduces a Maxwell boundary condition-based approach to derive system-environment coupling that accounts for polariton conservation in all coupling regimes.

Findings

Derived quantum Langevin equation and input-output relation from Maxwell's boundary conditions.

Established polariton conservation in system-environment coupling.

Applicable across weak to ultrastrong light-matter coupling regimes.

Abstract

In the standard theory of cavity quantum electrodynamics (QED), coupling between photons inside and outside a cavity (cavity system and photonic reservoir) is given conserving the total number of photons. However, when the cavity photons (ultra)strongly interact with atoms or excitations in matters, the system-reservoir coupling must be determined from a more fundamental viewpoint. Based on the Maxwell's boundary conditions in the QED theory for dielectric media, we derive the quantum Langevin equation and input-output relation, in which the total number of polaritons (not photons) inside the cavity and photons outside is conserved.