  We analyze the quantum dynamics of a superconducting cavity coupled to a
voltage biased Josephson junction. The cavity is strongly excited at resonances
where the voltage energy lost by a Cooper pair traversing the circuit is a
multiple of the cavity photon energy. We find that the resonances are
accompanied by substantial squeezing of the quantum fluctuations of the cavity
over a broad range of parameters and are able to identify regimes where the
fluctuations in the system take on universal values.
