Electroluminescence and multiphoton effects in a resonator driven by a tunnel junction

We study a transmission line resonator which is driven by electrons tunneling through a voltage-biased tunnel junction. Using the Born-Markovian quantum master equation in the polaren basis we investigate the nonequilibrium photon state and emission spectrum of the resonator as well as properties of the transport current across the tunnel junction and its noise spectrum. The electroluminescence is optimized, with maximum peak height and narrow linewidth, when the back-action of the tunnel junction on the resonator and the damping of the resonator are similar in strength. For strong coupling between the resonator and tunnel junction, multiphoton effects create signatures in the transport current and current noise spectrum.