Quantum dynamics of a Josephson junction driven cavity mode system in the presence of voltage bias noise

We give a semiclassical analysis of the average photon number as well as photon number variance (Fano factor F) for a Josephson junction (JJ) embedded microwave cavity system, where the JJ is subject to a fluctuating (i.e., noisy) bias voltage with finite dc average. Through the ac Josephson effect, the dc voltage bias drives the effectively nonlinear microwave cavity mode into an amplitude squeezed state (