Energy-band dynamics in a current-biased Josephson junction probed by incoherent Cooper-pair tunneling

We analyze how the dynamics in a current-biased mesoscopic Josephson junction can be probed by an additional smaller Josephson junction ( probe). The probe is connected to a small island in between the Josephson junction and a resistor R >> R(Q) = h/4e(2). The current through the resistor results in an effective current bias to the larger JJ. We model the steady state properties of the system under thermal and quantum fluctuations of the feed current. We use a density matrix approach based on the Born-Markov equations treating the current fluctuations perturbatively. The probe is also treated perturbatively assuming the regime of incoherent Cooper-pair tunneling. We find that the I-V characteristics across the probe shows traces of energy bands, Bloch oscillations and Zener tunneling in the current-biased Josephson junction.