From Few to Many Emitters Cavity QED: Energy Levels and Emission Spectra From Weak to Deep-Strong Coupling

TL;DR

This paper systematically investigates the energy levels and emission spectra of multiple quantum emitters coupled to a cavity across all light-matter interaction regimes, revealing how system properties evolve with increasing emitter number.

Contribution

It introduces a comprehensive theoretical framework for open cavity-QED systems applicable from weak to deep-strong coupling, including the thermodynamic limit and emitter-environment interactions.

Findings

Emergence of a cavity resonance peak for even numbers of emitters.

Convergence of many-emitter systems to two interacting bosonic modes.

Validation of gauge-invariant models across all coupling regimes.

Abstract

We present a systematic study of the properties of systems composed of $N$ two-level quantum emitters coupled to a single cavity mode, for light-matter interaction strengths ranging from the weak to the ultrastrong and deep-strong coupling regimes. Beginning with an analysis of the energy spectrum as a function of the light-matter coupling strength, we examine systems with varying numbers of emitters, from a pair to large collections, approaching the thermodynamic limit ($N \to \infty$). Additionally, we explore the emission properties of these systems under incoherent excitation of the emitters, employing a general theoretical framework for open cavity-QED systems, which is valid across all light-matter interaction regimes and preserves gauge invariance within truncated Hilbert spaces. Furthermore, we study the influence of the emitter-environment interaction on the spectral properties of the system. Specifically, when each emitter interacts independently with its own reservoir, we observe the emergence of an emission peak at the cavity's resonant frequency for even values of $N$. Our analysis also clarify the evolution of the system as the number of emitters increases, ultimately converging towards an equivalent system composed of two interacting single-mode bosonic fields.