Kerr coefficients of plasma resonances in Josephson junction chains

TL;DR

This paper combines experimental measurements and theoretical calculations to analyze the Kerr effects in plasma resonances of Josephson junction chains, providing insights into their nonlinear behavior and photon interactions.

Contribution

It introduces a method to calculate Kerr coefficients in Josephson junction chains and validates these calculations with experimental data.

Findings

Measured Kerr-induced frequency shifts match theoretical predictions.

Calibrated photon numbers using self-Kerr shifts.

Demonstrated linear dependence of frequency shift on photon number.

Abstract

We present an experimental and theoretical analysis of the self- and cross-Kerr effect of extended plasma resonances in Josephson junction chains. We calculate the Kerr coefficients by deriving and diagonalizing the Hamiltonian of a linear circuit model for the chain and then adding the Josephson non-linearity as a perturbation. The calculated Kerr-coefficients are compared with the measurement data of a chain of 200 junctions. The Kerr effect manifests itself as a frequency shift that depends linearly on the number of photons in a resonant mode. By changing the input power on a low signal level, we are able to measure this shift. The photon number is calibrated using the self-Kerr shift calculated from the sample parameters. We then compare the measured cross-Kerr shift with the theoretical prediction, using the calibrated photon number.