Multi-emitter oscillating bound states in Waveguide QED

TL;DR

This paper explores the formation and dynamics of superpositions of bound states in waveguide QED systems, revealing how non-local equilibrium states with persistent oscillations can be generated and controlled.

Contribution

It introduces a detailed analysis of hybrid bound states in waveguide QED, demonstrating their formation, conditions, and potential for emitter interaction and oscillatory photon modes.

Findings

Bound states coexist in the energy continuum and outside it, leading to hybrid oscillations.

Spontaneous emission can drive the system into non-local oscillatory equilibrium states.

Bound-state superpositions enable emitter interactions and oscillatory photon density modes.

Abstract

Waveguide quantum electrodynamics platforms have emerged as promising candidates for exploring and implementing non-Markovian quantum phenomena. In this work, we investigate the formation and dynamics of superpositions of bound states in a cavity array waveguide coupled to two spatially separated quantum emitters. By tuning the system parameters, we show that spontaneous emission can drive the system into non-local equilibrium states in which both photonic and emitter populations exhibit persistent oscillations. These states arise from the coexistence of bound states embedded in the energy continuum and bound states outside it, leading to hybrid oscillatory modes. We analytically derive the conditions required for the emergence of these states, numerically simulate their formation through spontaneous emission, and predict their long-time behaviour. Our results demonstrate that such bound-state superpositions enable the generation of emitter-emitter interaction through free evolution, while supporting oscillatory breathing modes of the photon density between the emitters.