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.

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• Cavity quantum electrodynamics
• Light-matter interaction
• Local density of states
• Nanophotonics
• Near-field optics
• Plasmonics
• Plasmons
• Polaritons
• Quantum states of light
• Surface plasmon polariton
• Metals
• Multilayer thin films
• Nanoparticles
• Quantum cavities
• Electromagnetic field calculations
• Green's function methods
• Two-level models