Adiabatic transport of Cooper pairs in arrays of Josephson junctions

TL;DR

This paper presents a quantitative theory of Cooper pair pumping in Josephson junction arrays, analyzing factors limiting accuracy and how supercurrent behavior scales with array size, relevant for quantum device applications.

Contribution

It introduces a detailed theoretical model for Cooper pair transport in Josephson arrays, highlighting quantum tunneling and supercurrent effects as key accuracy limitations.

Findings

Pumping accuracy decreases exponentially with array length due to tunneling and supercurrent effects.

Supercurrent at resonance scales as sin(v/N)/N, diminishing with array size.

Practical array sizes face fundamental accuracy limitations from quantum effects.

Abstract

We have developed a quantitative theory of Cooper pair pumping in gated one-dimensional arrays of Josephson junctions. The pumping accuracy is limited by quantum tunneling of Cooper pairs out of the propagating potential well and by direct supercurrent flow through the array. Both corrections decrease exponentially with the number N of junctions in the array, but give a serious limitation of accuracy for any practical array. The supercurrent at resonant gate voltages decreases with N only as sin(v/N)/N, where v is the Josephson phase difference across the array.