Experimental investigations of chaos-assisted tunneling in a microwave annular billiard

We present detailed investigations of the experimental signatures of chaos-assisted tunneling in the two-dimensional annular billiard, as already summarized in Phys. Rev. Lett. 84, 867 (2000). We have performed analog experiments with two-dimensional, electromagnetic resonators allowing for a direct simulation of the corresponding quantum system. Spectra from a superconducting cavity with a high-frequency resolution are combined with electromagnetic intensity distributions of high spatial resolution experimentally determined using a normal conducting twin cavity. Thereby all eigenmodes were obtained with properly identified quantum numbers. Besides distributions of quasi-doublet splittings, which serve as fundamental observables for the tunneling between whispering gallery types of modes, we also focus on the distributions of resonance widths of the doublets. These directly reflect the role of lifetime of certain modes in the tunneling process. Here, as theoretically expected, the class of so-called beach modes is found to play a particular role in mediating between regular and chaotic states to enhance the tunneling strength. This behavior is found in the spectrum and also in the structure of the wave functions.