Collective light-matter interaction in plasmonic waveguide quantum electrodynamics

Rabi oscillations characterize light-matter hybridization in the waveguide quantum electrodynamics~(WQED) framework, with their associated decay rates reflecting excitation damping, yet their behavior remains unresolved when collective emitters are coupled to a collective waveguide mode. This scenario reveals a conceptually novel collective-light-collective-matter interaction, realizable when a timed-Dicke state~(TDS) of subwavelength emitters couples to a slow, delocalized surface-plasmon mode, forming a hybridized plasmon-polariton~(HPP). The HPP acquires its directionality from the TDS via momentum matching. It also exhibits plasmonic characteristics, with excitation frequencies following the surface-plasmon dispersion relation. We obtain a Rabi oscillation and a long-time decay that describe the HPP and use them to reveal weak- and strong-coupling regimes through the emergence of normal-mode splitting. By performing a finite-time Lyapunov-exponent analysis, we show that the HPP also exhibits instantaneous decay and identify three distinct decay regimes: early-time rapid, transient-time oscillatory, and long-time classical. Finally, by analyzing the emission spectrum, we observe an anticrossing of the peak doublets~(a feature also seen in cavity QED setups) which originates from quantum vacuum effects and the resulting non-Markovian HPP evolution in our WQED.