Nonlinear wave chaos in superconducting billiards

The Random Coupling Model (RCM) has been shown to successfully predict the statistical properties of linear wave chaotic cavities in the highly over-moded regime. It is of interest to extend the RCM to strongly nonlinear systems. We have studied the statistics of harmonics generated in a billiard by a nonlinear circuit [1] and the case of a billiard with a single nonlinear port, both of which have a point-like nonlinearity. In this talk, we discuss measurements of the nonlinear S-parameters in superconducting billiards where the nonlinearity is continuously distributed. By taking advantage of the high power (up to +35 dBm) vector network analyzer (VNA), we observe that the S-parameters are power dependent. One billiard is a cut-circle quasi-2D microwave cavity which is made of Pb-plated copper. The granular Pb material has a dominant nonlinear resistance that manifests in the S-parameters We find the noise from the measurement setup affects the statistics in such a low loss system. Another billiard is the TiN on Si wafer billiard, where TiN is expected to have a dominant nonlinear reactance. We will present some preliminary results for this system. The goal is to study how the RCM can be extended to apply to nonlinear systems.
[1] Min Zhou, et al., Chaos 27, 103114 (2017).