Fluxon cotunneling in coupled Josephson junctions: Perturbation theory

TL;DR

This paper develops a perturbation theory to analyze fluxon cotunneling and Coulomb drag effects in coupled Josephson junctions, revealing how these phenomena depend on the coupling strength and providing predictions for experimental verification.

Contribution

It introduces a perturbation approach to calculate fluxon cotunneling amplitudes in coupled Josephson junctions and demonstrates the persistence of Coulomb drag at all non-zero coupling values.

Findings

Coulomb drag effect persists at any non-zero mutual capacitance.

Derived explicit fluxon cotunneling amplitudes for small mutual capacitance.

Predictions applicable to Josephson chains and testable in future experiments.

Abstract

We investigate the effects of fluxon cotunneling and quantum Coulomb drag in a system of two small Josephson junctions coupled by means of mutual capacitance $C_m$. Depending on the value of $C_m$ we identify three different regimes of strong, intermediate and weak coupling. Focusing our attention on the last two regimes we develop a perturbation theory in the interaction and explicitly derive fluxon cotunneling amplitudes at sufficiently small mutual capacitance values. We demonstrate that the Coulomb drag effect survives at any non-zero $C_m$ and evaluate the non-local voltage response that is in general determined by a trade off between two different cotunneling processes. Our predictions can be straightforwardly generalized to bilinear Josephson chains and directly verified in future experiments.