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We derive effective Hamiltonians for a single dipolar emitter coupled to ametal nanoparticle (MNP) with particular attention devoted to the role oflosses. For small particles sizes, absorption dominates and a non hermitianeffective Hamiltonian describes the dynamics of the hybrid emitter-MNPnanosource. We discuss the coupled system dynamics in the weak and strongcoupling regimes offering a simple understanding of the energy exchange,including radiative and non radiative processes. We define the plasmon Purcellfactors for each mode. For large particle sizes, radiative leakages cansignificantly perturbate the coupling process. We propose an effective FanoHamiltonian including plasmon leakages and discuss the link with thequasi-normal mode description. We also propose Lindblad equations for eachsituation and introduce a collective dissipator for describing the Fanobehaviour.

Non-hermitian Hamiltonian description for quantum plasmonics: from dissipative dressed atom picture to Fano states