Bloch band dynamics of a Josephson junction in an inductive environment

TL;DR

This study investigates how a Josephson junction's charge localization and Bloch band dynamics, influenced by an inductive SQUID array environment, affect its electrical properties, revealing complex quantum behaviors and energy renormalization effects.

Contribution

It provides a quantitative analysis of Bloch band dynamics and Landau-Zener transitions in a Josephson junction within an inductive environment, highlighting the impact on zero-bias resistance.

Findings

Charge localization enhances zero-bias resistance.

Bloch band diffusion and Landau-Zener transitions govern dynamics.

Self-resonant modes renormalize the Josephson energy.

Abstract

We have measured the current-voltage characteristics of a Josephson junction with tunable Josephson energy $E_J$ 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 understand this result quantitatively in terms of the Bloch band dynamics of the localized charge. This dynamics is governed by 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 $E_J$ of the tunable junction, which results in a renormalization of $E_J$, and, as a consequence, of the effective bandwidth of the lowest Bloch band.