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Plasmons in nanostructured metals are widely utilized to trigger stronglight--matter interactions with quantum light sources. While the nonclassicalbehavior of such quantum emitters (QEs) is well-understood in this context, therole of quantum and surface effects in the plasmonic resonator is usuallyneglected. Here, we combine the Green's tensor approach with the Feibelman$d$-parameter formalism to theoretically explore the influence of quantumsurface effects in metal-dielectric layered nanostructures on the relaxationdynamics of a proximal two-level QE. Having identified electron spill-out asthe dominant source of quantum effects in jellium-like metals, we focus ourstudy 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 thatstrong light--matter coupling is not suppressed by the emergence ofnonclassical surface effects in the optical response of the metal.

Quantum surface effects in strong coupling dynamics