Theory of Strong Coupling between Quantum Emitters and Propagating Surface Plasmons

Abstract

Here we present the theoretical foundation of the strong coupling phenomenon between quantum emitters and propagating surface plasmons observed in two-dimensional metal surfaces. For that purpose, we develop a quantum framework that accounts for the coherent coupling between emitters and surface plasmons and incorporates the presence of dissipation and dephasing. Our formalism is able to reveal the key physical mechanisms that explain the reported phenomenology and also determine the physical parameters that optimize the strong coupling. A discussion regarding the classical or quantum nature of this phenomenon is also presented. DOI: 10.1103/PhysRevLett.110.126801 PACS numbers: 73.20.Mf, 42.50.Nn, 71.36.+c Surface plasmon polaritons (SPPs), hybrid bound modes comprising both electromagnetic fields and charge currents, are well known to have both a subwavelength confinement and propagation lengths of tens or even hundreds of wavelengths [1,2]. For this reason, the interaction between quantum emitters (QEs) and SPPs has attracted great interest recently [3][4][5]. It has been shown that QE-SPP coupling can lead to single SPP generation [6][7][8] and that the interaction between two QEs can be mediated by SPPs, resulting in energy transfer, superradiance [9], and entanglement phenomena [10][11][12]. Recently, there have also been several experimental studies that show the emergence of strong coupling (SC), i.e., coherent energy exchange between propagating SPPs and excitons either in organic molecules [13][14][15][16][17][18] or in quantum dots [19][20][21]. However, to our knowledge, a first-principles explanation of these experimental results has not been presented yet.In this Letter, we analyze the phenomenon of SC between quantum emitters (or absorbers) and SPPs and present its theoretical foundation. We develop a complete quantum treatment that is not only able to calculate absorption spectra and reproduce the experimental phenomenology but also deal with more complex aspects such as photon statistics.In Fig. 1(a) we render a sketch of the general structure that mimics the experimental configuration: a collection of N QEs immersed into a layer of thickness W and placed on top of a thin metal film (thickness h). In this work, the acronym QE will refer to a quantum system with discrete electronic levels, like organic molecules or quantum dots. In some of the experimental setups and in order to avoid quenching of the QEs, a dielectric spacer of width s is located between the QEs and the metal substrate. We will take 2 ¼ 1 ¼ 1 in our calculations, and we will use the dielectric function of the metal (silver) m as tabulated in Ref. [22]. As a minor simplification, we will assume a semi-infinite metal substrate instead of the metal film considered in the experiments (these films are thick enough for the SPPs to be very similar to those of a single interface). Each QE is represented by a two-level system (2LS) fjgi; jeig and characterized by a transition frequency ! 0 (in this Letter we will use ! 0 ¼ 2 eV, @ ¼ 1...

Spatial Coherence Properties of Organic Molecules Coupled to Plasmonic Surface Lattice Resonances in the Weak and Strong Coupling Regimes

“…2(c)-(e), 2(h)-2(j), and 2(m)-2(o) for different arrays and are in good agreement with the experimentally observed mode energies. The SLR-exciton coupling is expected to scale as ffiffiffiffiffiffiffiffiffi ffi N=V p , where N is the number of molecules and V is the mode volume [26,27]: this is confirmed in Fig. 2(p).…”

Cavity-Enhanced Transport of Charge

“…PACS numbers: 05.60. Gg, 42.50.Pq, 74.40.Gh, The study of strong light-matter interactions [1][2][3][4] is playing an increasingly crucial role in understanding as well as engineering new states of matter with relevance to the fields of quantum optics [5][6][7][8][9][10][11][12][13][14][15][16][17][18], solid state physics [19][20][21][22][23][24][25][26][27][28][29][30][31], as well as quantum chemistry [32][33][34][35][36] and material science [37][38][39][40][41][42][43][44][45][46][47][48][49][...…”

Transformation Optics Approach to Plasmon-Exciton Strong Coupling in Nanocavities

“…From the experimental side, in recent years, PEPs have been reported in emitter ensembles [10][11][12][13], in which excitonic nonlinearities are negligible [14][15][16]. Only very recently, thanks to advances in the fabrication and characterization of large Purcell enhancement nanocavities [17][18][19], far-field signatures of plasmonexciton strong coupling for single molecules have been reported experimentally [20].…”