Inhomogeneous Josephson junction chains for superinductance optimization

TL;DR

This study investigates how spatial variations in Josephson junction chains affect their inductance and low-frequency behavior, finding that homogeneous chains are optimal unless tunable SQUIDs are used, with benefits diminishing for longer chains.

Contribution

It provides a theoretical analysis of inhomogeneous Josephson chains, showing that homogeneous configurations are optimal unless tunable SQUIDs are employed for parameter variation.

Findings

Homogeneous chains maximize inductance without reducing low-frequency window.

Using SQUIDs with different loop areas offers some improvement.

Benefits of inhomogeneity decrease as chain length increases.

Abstract

We report a theoretical study of the low-frequency impedance of a Josephson junction chain whose parameters vary in space. Our goal is to find the optimal spatial profile which maximizes the total inductance of the chain without shrinking the low-frequency window where the chain behaves as an inductor. If the spatial modulation is introduced by varying the junction areas, we find that the best result is obtained for a spatially homogeneous chain, reported earlier in the literature. An improvement over the homogeneous result can be obtained by representing the junctions by SQUIDs with different loop areas, so the inductances can be varied by applying a magnetic field. Still, we find that this improvement becomes less important for longer chains.