Adiabatic elimination for ensembles of emitters in cavities with dissipative couplings

TL;DR

This paper develops an adiabatic elimination method for ensembles of cavity-coupled two-level emitters with both coherent and dissipative interactions, deriving effective equations for a single emitter-cavity subsystem to improve understanding of cavity-emitter coupling.

Contribution

It introduces a new adiabatic elimination approach for systems with dissipative couplings, enabling simplified analysis of cavity-emitter interactions.

Findings

Effective equations for cavity and single emitter derived

Limitations of subsystem parameters analyzed

Impact of dissipative decay on cavity transmission studied

Abstract

We consider an ensemble of cavity-coupled two-level emitters interacting via full (coherent and dissipative) dipole-dipole interactions. Using an adiabatic elimination procedure we derive effective equations of motion for a subsystem consisting of the cavity and a single emitter. Those equations can be used for schemes to enhance the cavity-coupling of single emitters as shown in [S. Sch\"{u}tz, J. Schachenmayer, D. Hagenm\"{u}ller, G. K. Brennen, T. Volz, V. Sandoghdar, T. W. Ebbesen, C. Genes, and G. Pupillo, e-print arXiv:1904.08888]. We analyze limitations of effective subsystem parameters, and study how joint dissipative decay processes in the subsystem affect cavity-coupling properties of the single emitter and cavity transmission spectra.