Kerr non-linearity in a superconducting Josephson metamaterial

TL;DR

This paper provides a comprehensive experimental and theoretical study of Kerr non-linearity in a superconducting Josephson metamaterial, demonstrating precise agreement between measurements and models for plasma modes and Kerr shifts.

Contribution

It offers the first detailed analysis of dispersion and Kerr frequency shifts in a long Josephson junction chain, incorporating long-range charge screening effects.

Findings

Measured dispersion curve matches theoretical predictions.

Observed and quantified self- and cross-Kerr shifts for multiple modes.

Good agreement between measured Kerr coefficients and theoretical models.

Abstract

We present a detailed experimental and theoretical analysis of the dispersion and non-linear Kerr frequency shifts of plasma modes in a one-dimensional Josephson junction chain containing 500 SQUIDs in the regime of weak nonlinearity. The measured low-power dispersion curve agrees perfectly with the theoretical model if we take into account the Kerr renormalisation of the bare frequencies and the long-range nature of the island charge screening by a remote ground plane. We measured the self- and cross-Kerr shifts for the frequencies of the eight lowest modes in the chain. We compare the measured Kerr coefficients with theory and find good agreement.