Impact of nonradiative line broadening on emission in photonic and plasmonic cavities

A light-matter interaction modified by the material environment is one of the central topics in quantum electrodynamics. While a strong coupling between a single emitter and a cavity and the Markovian (exponential) relaxation regime are most straightforwardly covered by theory, real physical systems that include also various line broadening effects may possess a much more complicated behavior. Here we propose a theoretical framework to account for nonradiative interaction effects in emission in photonic and plasmonic cavities. The quantum electrodynamics model formulated via a stochastic Hamiltonian approach has been developed with nonradiative line broadening introduced via the Kubo oscillator model. The impact of competing radiative and nonradiative processes on the emitter dynamics has been studied, showing that nonradiative relaxations, having significant impact on processes in high-$Q$ photonic cavities, are much less influential in the plasmonic regime. The developed theoretical framework is not restricted to the emitter in a cavity example, but represents a general tool for multiple stochastic Hamiltonian evolution, important for various types of interactions where either classical or quantum noise is present.

Figure 1

Schematic representations of an emitter in (a) photonic and (b) plasmonic cavities. The inset shows a two-level emitter with natural and nonradiative line broadenings.

Figure 2

Dependence of the time evolution of an emitter in a photonic cavity on a cavity quality factor: (a) and (c) probability of the two-level system being in the excited state and (b) and (d) number state of the cavity photon. The emitter (a) and (b) without and (c) and (d) with nonradiative broadening has been considered.

Figure 3

Dependence of the time evolution of an emitter in a plasmonic cavity on a cavity modal volume: (a) and (c) probability of the two-level system being in the excited state and (b) and (d) number state of the cavity plasmon for (a) and (b) $Q=100$ and (c) and (d) $Q=1000$. The emitter without and with nonradiative broadening exhibits similar behavior.