Bloch band dynamics of a Josephson junction in an inductive environment

We have measured the current-voltage characteristics of a Josephson junction with tunable Josephson energy EJ embedded in an inductive environment provided by a chain of SQUIDs. Such an environment induces localization of the charge on the junction, which results in an enhancement of the zero-bias resistance of the circuit. We explain this result quantitatively in terms of the Bloch band dynamics of the localized charge. This dynamics is governed by charge diffusion in the lowest Bloch band of the Josephson junction as well as by Landau-Zener transitions out of the lowest band into the higher bands. In addition, the frequencies corresponding to the self-resonant modes of the SQUID array exceed the Josephson energy EJ of the tunable junction, which results in a renormalization of EJ, and, as a consequence, an increase of the effective bandwidth of the lowest Bloch band.