  Motivated by recent experiments on superconducting circuits consisting of a
dc-voltage biased Josephson junction in series with a resonator, quantum
properties of these devices far from equilibrium are studied. This includes a
crossover from a domain of incoherent to a domain of coherent Cooper pair
tunneling, where the circuit realizes a driven nonlinear oscillator.
Equivalently, weak photon-charge coupling turns into strong correlations
captured by a single degree of freedom. Radiated photons offer a new tool to
monitor charge flow and current noise gives access to nonlinear dynamics, which
allows to analyze quantum-classical boundaries.
