Hybrid molecular-plasmonic nanostructures have demonstrated their potential for surface enhanced spectroscopies, sensing or quantum control at the nanoscale. In this work, we investigate the strong coupling regime and explicitly describe the hybridization between the localized plasmons of a metal nanoparticle and the excited state of a quantum emitter, offering a simple and precise understanding of the energy exchange in full analogy with cavity quantum electrodynamics treatment and dressed atom picture. Both near field emission and far field radiation are discussed, revealing the richness of such optical nanosources.Optical microcavities can store light for a long time allowing efficient light-matter interaction with important applications in quantum technologies, low threshold laser [1], supercontinuum laser [2] or indistinguishable single photon source [3]. It relies on the extremely high quality factor of the cavity mode but at the price of diffraction limited sizes. That is why strong efforts have be done since a decade to transpose cavity quantum electrodynamics (cQED) concepts to nanophotonics and plasmonics [4][5][6][7][8]. Particular attention has been devoted to the strong coupling regime [9][10][11][12] since it offers the possibility of a control dynamics of the light emission, as e.g. photon blockade [13,14] or coherent control [15,16].In this letter, we build an effective Hamiltonian that fully transposes the cQED description to an hybrid plasmon-quantum emitter nanosource. We demonstrate it can be exactly described in full analogy with cQED representation. Specifically, the coupled plasmon-emitter system behaves like an emitter in a multimodal lossy cavity. We notably determine the structure of the emitter states dressed by the plasmon modes.We consider the hybrid system displayed in Fig. 1. A two level system (TLS) quantum emitter is located close to a metal nanoparticle (MNP). The optical transition is characterized by the frequency ω eg , the dipole moment d eg and the operatorσ † eg = |g e|. For the sake of clarity, we consider a TLS emitter coupled to spherical MNP since the localized surface plasmon (LSP) modes involved in the coupling process are well identified and the hybridization of the emitter and MNP modes will be unambiguously demonstrated. * gerard.colas-des-francs@u-bourgogne.fr The Hamiltonian of the coupled system writeŝThe first term refers to the TLS energy and we have phenomelogically introduced the decay rate of the excited state γ d in the second term.The third term describes the total energy of the electromagnetic field wheref † (f ) is the LSP polaritonic vector field operator associated to the creation (annihilation) of a quantum of electromagnetic mode in presence of the MNP. The last term describes the emitter-field interaction under the rotatingwave approximation.The electromagnetic field has to be quantized by taking into account the dispersing and absorbing nature of the metal [17][18][19]. The electromagnetic mode dispersion and absorption are governed by the real a...

We derive effective Hamiltonians for a single dipolar emitter coupled to a metal nanoparticle (MNP) with particular attention devoted to the role of losses. For small particles sizes, absorption dominates and a non hermitian effective Hamiltonian describes the dynamics of the hybrid emitter-MNP nanosource. 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. For large particle sizes, radiative leakages can significantly perturbate the coupling process. We propose an effective Fano Hamiltonian including plasmon leakages and discuss the link with the quasinormal mode description. We also propose Lindblad equations for each situation and introduce a collective dissipator for describing the Fano behaviour.