Quantum and Wave Dynamical Chaos in Superconducting Microwave Billiards

TL;DR

This paper reviews two decades of research on quantum and wave dynamical chaos in superconducting microwave billiards, highlighting experimental results on eigenvalue fluctuations, wave chaos in 3D cavities, dynamical tunneling, and studies of artificial graphene.

Contribution

It provides a comprehensive overview of experimental findings and introduces new approaches to understanding dynamical tunneling and artificial graphene in microwave systems.

Findings

Universal fluctuation properties of eigenvalues in chaotic systems

Wave-dynamical chaos observed in three-dimensional microwave cavities

New insights into dynamical tunneling phenomena

Abstract

Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with flat, cylindrical microwave resonators, so-called microwave billiards, concerning the universal fluctuation properties of the eigenvalues of classically chaotic systems with no, a threefold and a broken symmetry; (ii) summarize our findings concerning the wave-dynamical chaos in three-dimensional microwave cavities; (iii) present a new approach for the understanding of the phenomenon of dynamical tunneling which was developed on the basis of experiments that were performed recently with unprecedented precision, and finally, (iv) give an insight into an ongoing project, where we investigate universal properties of (artificial) graphene with superconducting microwave photonic crystals that are enclosed in a microwave resonator, i.e., so-called Dirac billiards.