  We consider the coupling of a single mode microwave resonator to a tunnel
junction whose contacts are at thermal equilibrium. We derive the quantum
master equation describing the evolution of the resonator field in the strong
coupling regime, where the characteristic impedance of the resonator is larger
than the quantum of resistance. We first study the case of a
normal-insulator-normal junction and show that a dc driven single photon source
can be obtained. We then consider the case of a superconductor-insulator-normal
and superconductor-insulator-superconductor junction. There, we show that the
Lamb shift induced by the junction gives rise to a nonlinear spectrum of the
resonator even when the junction induced losses are negligible. We discuss the
resulting dynamics and consider possible applications including quantum Zeno
dynamics and the realization of a qubit.
