Photon-Emission Statistics induced by Electron Tunnelling in Plasmonic Nanojunctions

TL;DR

This paper analyzes photon emission statistics in plasmonic nanojunctions caused by electron tunneling, revealing how waiting-time distributions provide unique insights beyond traditional correlation functions.

Contribution

It introduces the use of waiting-time distribution $w( au)$ to analyze photon emission, offering new physical insights in plasmonic nanojunctions beyond standard $g^{(2)}( au)$ analysis.

Findings

Waiting-time distribution reveals average delay of 1/$\Gamma$ in photon emission.

$w( au)$ provides independent information from $g^{(2)}( au)$ about emission dynamics.

Analysis remains effective despite imperfect photon detection.

Abstract

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.