Single-photon emission mediated by single-electron tunneling in plasmonic nanojunctions

International audience−3 −2 −1 0 1 2 3 eV L /ωc −1.0 −0.5 0.0 0.5 1.0 −I/eΓ λ = 0.1 λ = 0.3 λ = 0.6 λ = 0.8 λ = 1.4 λ = 2.0 λ = 0.8 λ = 1.4 λ = 2.0Recent scanning tunneling microscopy (STM) experiments reported single-molecule fluorescence induced by tunneling currents in the nanoplasmonic cavity formed by the STM tip and the substrate. The electric field of the cavity mode couples with the current-induced charge fluctuations of the molecule, allowing the excitation of photons. We investigate theoretically this system for the experimentally relevant limit of large damping rate κ for the cavity mode and arbitrary coupling strength to a single-electronic level. We find that for bias voltages close to the first inelastic threshold of photon emission, the emitted light displays antibunching behavior with vanishing second-order photon correlation function. At the same time, the current and the intensity of emitted light display Franck-Condon steps at multiples of the cavity frequency ω c with a width controlled by κ rather than the temperature T. For large bias voltages, we predict strong photon bunching of the order of κ=Γ where Γ is the electronic tunneling rate. Our theory thus predicts that strong coupling to a single level allows current-driven nonclassical light emission. Electronic transport coupled to the field of an electromagnetic cavity can be realized in a wealth of different systems. This includes in the microwave range carbon nanotubes [1-5], quantum dots [6-9], and Josephson junctions [10-12], or in the optical range, molecules in plasmonic nanocavities formed by an STM tip with a substrate [13-24] and organic microcavities [25-27], or with waveguide quantum electrodynamic systems [28-30]. The reduction of the cavity volume V results in an increase of the zero-point quantum fluctuations of the electric field E zpm ∼ V −1=2. This motivated optical studies of molecular two-level systems strongly coupled to the cavity field by the dipolar interaction Λ d ∼ pE zpm , (with p the molecule dipole moment). One of the goals of this effort is to reach Λ d larger than κ, which has been and remains challenging, despite recent achievements [31]. On the other side, the coupling of a cavity mode to the current-induced charge fluctuations of a single-electronic level is given by a monopolar coupling constant Λ m ∼ eLE zpm as derived in Ref. [32] (see also Ref. [33]), with L the typical extension of the transport region and e the electronic charge. Since typically in a given system eL ≫ p, the monopolar coupling constant is much larger than the dipolar one [32]. This probably contributed to the observation of values of Λ m larger than κ in microwave cavities coupled to electronic transport [4,6,8] and even approaching the cavity resonating frequency ω c (ℏ ¼ 1) [11,39,40]. Recent results in plas-monic cavities coupled to electronic transport [17,21,22] thus open the possibility to explore transport through a single electronic level in these structures. This is expected to reach much larger coupling constants than those currently observed for purely dipolar coupling, requiring further theoretical investigations. The system presents strong analogies with electron transport coupled to molecular vibrations. This has been investigated in different regimes, leading to the striking prediction of the Franck-Condon blockade [34,41,42] and its observation [35,43]. However, there are important differences. The first is the low quality factor of plasmonic cavities, which is typically of the order of 10 [31]. The second, and more interesting, is that the state of the optical or microwave cavity can be directly measured by detecting the emitted photons. It is thus important to investigate how transport through a molecule is linked to the property of the emitted radiation [44-46]. In this Letter we consider electronic transport through a single-level quantum dot, where the charge on the dot is coupled to the electric field of an electromagnetic cavity. We propose a theoretical model to obtain the current through the quantum dot taking into account the cavity dissipation κ, and arbitrary values of the coupling strength in the incoherent transport regime Γ ≪ k B T, with Γ the electron tunneling rate, T the temperature, and k B th