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

Abstract

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.

Understanding radiative transitions and relaxation pathways in plexcitons

“…Given the electronic structure of the individual components, and the expected coupling between them, we arrived at the energy level structure shown in Figure 1A. We summarize the state energies and couplings in the following Hamiltonian, which is analogous to that proposed by others [58][59][60][61][62] (see Figure 1A). The Hamiltonian in the {g, p 1 , J 1 } basis (that we call here site basis) reads:…”

Macroscopic QED for quantum nanophotonics: emitter-centered modes as a minimal basis for multiemitter problems

“…Following references [39][40][41][42][43][44], we now look for a linear transformation of the bosonic modes f λ (r, ω) at each frequency in such a way that in the new basis, only a minimal number of EM modes couples to the emitters. To this end, we start with the macroscopic QED Hamiltonian within the multipolar approach Eq.…”

“…We mention for completeness that if the dark modes are initially excited, including them might be necessary to fully describe the state of the system. We have now explicitly constructed a Hamiltonian with only N independent EM modes C i (ω) for each frequency ω [39][40][41][42][43][44]. This Hamiltonian corresponds to a set of N emitters coupled to N continua and can be treated using, e.g., a wide variety of methods developed in the context of open quantum systems [84][85][86][87].…”

“…We then review in detail a somewhat nonstandard formulation of macroscopic QED that allows one to construct a minimal quantized basis for the EM field interacting with a collection of multiple quantum emitters. This approach was first introduced by Buhmann and Welsch [39] and subsequently rediscovered independently by several other groups [40][41][42][43][44]. The fact that this very useful approach has been reinvented by different researchers over the past decade or so partially motivates the current article, which intends to give a concise and accessible overview, and presents some explicit relations that have (to our knowledge) not been published before.…”

Strong coupling as an interplay of quantum emitter hybridization with plasmonic dark and bright modes

“…Alternatively, strong coupling between the QE and the so-called "dark," weakly radiative modes of conventional Ag and Au nanoparticles has been explored [30][31][32][33][34][35][36][37]. Despite the fact these dark modes are not observable using traditional optical techniques (although they can be observed by electron energy loss spectroscopy (EELS) [38][39][40][41][42], or in scattered light by large clusters [43] and anapoles [44]), it might be possible to visualize them by further hybridization of the dark mode-QE state with the bright mode of the resonator.…”