Quantum surface effects in strong coupling dynamics

Plasmons in nanostructured metals are widely utilized to trigger strong light--matter interactions with quantum light sources. While the nonclassical behavior of such quantum emitters (QEs) is well-understood in this context, the role of quantum and surface effects in the plasmonic resonator is usually neglected. Here, we combine the Green's tensor approach with the Feibelman $d$-parameter formalism to theoretically explore the influence of quantum surface effects in metal-dielectric layered nanostructures on the relaxation dynamics of a proximal two-level QE. Having identified electron spill-out as the dominant source of quantum effects in jellium-like metals, we focus our study on sodium. Our results reveal a clear splitting in the emission spectrum, indicative of having reached the strong-coupling regime, and, more importantly, non-Markovian relaxation dynamics of the emitter. Our findings establish that strong light--matter coupling is not suppressed by the emergence of nonclassical surface effects in the optical response of the metal.