Photon-mediated interactions and dynamics of coherently driven quantum emitters in complex photonic environments

TL;DR

This paper assesses the validity of traditional photon-mediated interaction models for quantum emitters in complex photonic environments, especially beyond typical assumptions, using a hybrid cavity system as a test case.

Contribution

It benchmarks the accuracy of the Born-Markov master equation approach against exact calculations in structured photonic environments, revealing regimes of model validity.

Findings

Effective models are accurate in certain regimes of laser driving and frequency splitting.

Complex photonic environments can significantly challenge traditional modeling assumptions.

The study identifies four regimes with different levels of model accuracy.

Abstract

In recent years, Born-Markov master equations based on tracing out the electromagnetic degrees of freedom have been extensively employed in the description of quantum optical phenomena originating from photon-mediated interactions in quantum emitter ensembles. The breakdown of these effective models, built on assumptions such as ensemble spectral homogeneity, an unstructured photonic density of states, and weak light-matter coupling, has also recently attracted considerable attention. Here, we investigate the accuracy of this well-established framework beyond the most conventional, and extensively explored, spontaneous emission configuration. Specifically, we consider a system comprising two coherently driven and detuned quantum emitters, embedded within a hybrid photonic-plasmonic cavity, formed by a metallic nanorod integrated into a high-refractive-index dielectric microresonator. The local density of photonic states in this structure exhibits a complex frequency dependence, making it a compelling platform for exploring photon-mediated interactions beyond the assumptions above. We benchmark this modeling approach for the quantum dynamics of the emitter pair against exact calculations based on a macroscopic field quantization formalism, providing an illustrative assessment of its validity in significantly structured and dispersive photonic environments. Our analysis reveals four distinct regimes of laser driving and frequency splitting that lead to markedly different levels of accuracy in the effective model.