Cooperative emission of light by an ensemble of dipoles near a metal nanoparticle: The plasmonic Dicke effect

Abstract

We identify a new mechanism for cooperative emission of light by an ensemble of N dipoles near a metal nanostructure supporting a surface plasmon.The cross-talk between emitters due to virtual plasmon exchange leads to a formation of three plasmonic super-radiant modes whose radiative decay rates scales with N , while the total radiated energy is thrice that of a single emitter. Our numerical simulations indicate that the plasmonic Dicke effect survives non-radiative losses in the metal.Radiation of a dipole near a metal nanostructure supporting surface plasmon (SP) is attracting renewed interest due to possible biosensing applications [1]. While early studies mainly focused on fluorescence of molecules near rough metal films [2], recent advances in near-field optics and in chemical control of molecule-nanostructure complexes spurred a number of experiments on single metal nanoparticles (NP) linked to dye molecules [3,4,5,6,7,8] or semiconductor quantum dots [9]. Emission of a photon by a dipole-NP complex involves two competing processes: enhancement due to resonance energy transfer (RET) from an excited dipole to a SP [10], and quenching due to decay into optically-inactive excitations in the metal [11]. These decay channels are characterized by radiative, Γ r , and non-radiative, Γ nr , decay rates, respectively, and their balance is determined by the separation, d, of the emitter from the metal surface [12,13]. The emission is most enhanced at some optimal distance, and is quenched close to the NP surface due to the suppression of quantum efficiency, Q = Γ r / (Γ r + Γ nr ), by prevalent non-radiative processes. Both enhancement and quenching were widely observed in fluorescence experiments on Au and Ag nanoparticles [3,4,5,6,7,8]. In recent single-molecule measurements [6,7,8], the distance dependence was in a good agreement with single-dipole-NP models [12,13], prompting proposals for a NP-based nanoscopic ruler [8].In this Letter, we identify a novel mechanism in the emission of light by an ensemble of dipoles located near a nanostructure supporting a localized SP. A typical setup would involve, e.g., dye molecules [3,4,5] or quantum dots [9] attached to a metal NP via DNA linkers. Namely, we demonstrate that RET between individual dipoles and SP leads to a cross-talk between the emitters. As a result, the emission of a photon becomes a cooperative process involving all dipoles in the ensemble. This plasmonic mechanism of cooperative emission is analogous to the Dicke effect for N radiating dipoles in free space, confined within a volume with characteristic size smaller than the radiation wavelength λ [14,15,16]. In that case, the cooperative emission is due to photon exchange between the emitters that gives rise to super-radiant (SR) states with total angular momentun 1 and enhanced radiative decay rate ∼ N Γ r 0 , where Γ r 0 is the decay rate of an isolated dipole. In contrast, in plasmonic systems, the dominant coupling mechanism between dipoles is SP exchange, i.e., excitation of a virtual SP in a na...

Spaser quenching by off-resonant plasmon modes

“…For a QE oriented normally to spherical NP surface, these rates have the form [25][26][27][28] Γ r = γ 0 r 1 +…”

“…Even though a metal nanostructure possesses discrete spectrum of localized plasmon modes, e.g., characterized by angular momentum l for spherical systems, the QE coupling to off-resonant modes well separated in frequency from QE (and from resonant mode) is usually considered sufficiently weak and, hence, neglected [3,[20][21][22][23][24]. However, while this is a good approximation for high-quality cavity modes, the plasmon resonances are characterized by much broader bands due to large Ohmic losses in metal, so that a significant fraction of excited QE energy is transferred to off-resonant modes, especially for small QE distances to the metal surface and, correspondingly, large QE-plasmon coupling [25][26][27][28]. In plasmonenhanced fluorescence spectroscopy, such processes lead to distance-dependent radiation quenching , characterized by quantum efficiency Q = Γ r /(Γ r + Γ nr ), where Γ r is plasmon-enhanced radiative decay rate and Γ nr is nonradiative decay rate due to QE coupling to higher-order modes (see below for detail).…”

“…In this case, a major source of dephasing in NPbased spasers is the ET between gain and off-resonant plasmon modes which is largely insensitive to QE dipole orientations. Although the ET rate between a QE and off-resonant modes is normally significantly lower than between QE and resonant mode, the number of excited modes increases exponentially as the QE distance to NP surface is reduced [25][26][27][28], which leads to significant fluorescence quenching for distances below NP radius (see Fig. 1).…”

Analog of superradiant emission in thermal emitters

“…The superradiance has been an active field in atomic physics for decades [25][26][27]. Recently, it has also been studied in classical optics in the context of electromagnetically induced transparency [28,29], Fano interference [30][31][32] and in complex radiation environments [33][34][35][36]. The analog of superradiance has never been considered to be present in thermal emitters, which is vaguely justified since the underlying process of thermal radiation is an incoherent process.…”

Interaction-free evolving states of a bipartite system

“…In such a general dynamical scenario the increasing attention to the existence in some bipartite systems of subradiant states that are selected pure factorized states which evolve, keeping the system in its fully initial decorrelated condition at any time instant, is not surprising. Such peculiar behavior, of both fundamental [1,2] and applicative interest [3][4][5][6][7][8], results from quantum interference effects canceling in the evolved state, at a generic time instant, exactly those contributions, stemming from the superposition principle, which, otherwise, would determine the onset and possibly the persistence of correlation manifestations between A and B. Subradiance is a cooperative effect that has been investigated both theoretically [1,2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and experimentally [4,[27][28][29][30][31][32] following the seminal paper by Dicke [1], mainly in radiation-matter systems, where it describes optically inactive states of an atomic ensemble (A) in an electromagnetic environment (B). The current upsurge of interest in these states reflects, indeed, the existence of many other physical contexts where this phenomenon may find promising applications [4,[33][34]…”