Arrays of Josephson junctions in an environment with vanishing impedance

TL;DR

This paper develops a Hamiltonian model for arrays of Josephson junctions considering charging effects and gate voltages, providing explicit predictions for supercurrent and pumped current with renormalization to account for inhomogeneity.

Contribution

It introduces a Hamiltonian framework for Josephson junction arrays that includes renormalization to handle inhomogeneity and non-ideal gating, offering testable predictions.

Findings

Explicit prediction of supercurrent and pumped current.

Renormalization accounts for array inhomogeneity.

Model based on experimentally accessible parameters.

Abstract

The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunnelling and charging effects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discussed with an emphasis on the inaccuracies in the Cooper pair pumping. Renormalisation of the Hamiltonian operator is used in order to reliably parametrise the effects due to inhomogeneity in the array and non-ideal gating sequences. The relatively simple model yields an explicit, testable prediction based on three experimentally motivated and determinable parameters.