cQED-like description for quantum plasmonics: from dissipative dressed atom picture to Fano states

We derive a plasmon-dressed atom picture for a single dipolar emitter coupled to a metal nanoparticle, in full analogy with cavity quantum electrodynamics and a dressed atom picture of the atom-field interaction. We obtain an anharmonic Jaynes-Cummings ladder where anharmonicity originates from the number of plasmons involved in the coupling process. We discuss the coupled system dynamics in the weak and strong coupling regimes offering a simple understanding of the energy exchange, including radiative and non radiative processes. We define the plasmon Purcell factors for each mode. Finally, we investigate the effect of leakages on the system dynamics. We propose an effective Fano Hamiltonian including plasmon leakages and discuss the link with the quasi-normal mode description.