  We consider 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 polaron 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
decay rate of the resonator are similar in strength. For strong coupling
between the resonator and tunnel junction, multi-photon effects show up in the
noise spectrum of the transport current.
