Photon-Emission Statistics induced by Electron Tunnelling in Plasmonic Nanojunctions

We investigate the statistics of photons emitted by tunneling electrons in a single electronic level plasmonic nanojunction. We compute the waiting-time distribution of successive emitted photons $w(\tau)$. When the cavity damping rate $\kappa$ is larger than the electronic tunneling rate $\Gamma$, we show that in the photon-antibunching regime, $w(\tau)$ indicates that the average delay-time between two successive photon emission events is given by $1/\Gamma$. This is in contrast with the usually considered second-order correlation function of emitted photons, $g^{(2)}(\tau)$, which displays the single time scale $1/\kappa$. Our analysis shows a relevant example for which $w(\tau)$ gives independent information on the photon-emission statistics with respect to $g^{(2)}(\tau)$, leading to a physical insight on the problem. We discuss how this information can be extracted from experiments even in presence of a non-perfect photon detection yield.