Weak and strong-coupling dynamics of quantum emitters in the vicinity of metallic films: role of electron spill-out

The relaxation of a quantum emitter (QE) near metal-dielectric layered nanostructures is investigated, with focus on the influence of plasmonic quantum effects. The Green's tensor approach, combined with the Feibelman $d$-parameter formalism, is used to calculate the Purcell factor and the dynamics of a two-level QE in the presence of the nanostructure. Focusing on the case of Na, we identify electron spill-out as the dominant source of quantum effects in jellium-like metals. Our results reveal a clear splitting in the emission spectrum of the emitter, and non-Markovian relaxation dynamics, implying strong light--matter coupling between them, a coupling that is not prevented by the quantum-informed optical response of the metal.