Nonlinearity of transparent SNS weak links decreases sharply with length

TL;DR

This paper demonstrates that increasing the length of SNS weak links significantly reduces their nonlinearity, offering a new parameter for designing low-nonlinearity microwave circuits, with implications for quantum technologies.

Contribution

It reveals the strong suppression of nonlinearity with finite SNS junction length and connects this to nonanalytic length dependence, providing a new design parameter for microwave circuits.

Findings

Nonlinearity decreases sharply with junction length.

Suppression factor can reach up to ten.

Length influences anharmonicity bounds.

Abstract

Superconductor-normal material-superconductor (SNS) junctions are being integrated into microwave circuits for fundamental and applied research goals. The short junction limit is a common simplifying assumption for experiments with SNS junctions, but this limit constrains how small the nonlinearity of the microwave circuit can be. Here, we show that a finite length of the weak link strongly suppresses the nonlinearity compared to its zero-length limit -- the suppression can be up to a factor of ten even when the length remains shorter than the induced coherence length. We tie this behavior to the nonanalytic dependence of nonlinearity on length, which the critical current does not exhibit. Further, we identify additional experimentally observable consequences of nonzero length, and we conjecture that anharmonicity is bounded between zero and a maximally negative value for any non-interacting Josephson junction in the presence of time-reversal symmetry. We promote SNS junction length as a useful parameter for designing weakly nonlinear microwave circuits.