First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard

Abstract

We report on first experimental signatures for chaos-assisted tunneling in a two-dimensional annular billiard. Measurements of microwave spectra from a superconducting cavity with high frequency resolution are combined with electromagnetic field distributions experimentally determined from a normal conducting twin cavity with high spatial resolution to resolve eigenmodes with properly identified quantum numbers. Distributions of quasidoublet splittings serve as basic observables for the tunneling between whispering gallery-type modes localized to congruent, but distinct tori which are coupled weakly to irregular eigenstates associated with the chaotic region in phase space.

Influence of classical resonances on chaotic tunneling

“…Moreover, it is one of its signatures that chaotic tunnelling can be modified on several orders of magnitude by the slightest variation of any classical or quantum parameter; therefore a deep understanding of chaotic tunnelling is required to control the process, what may be an advantage in delicate quantum experiments and, hopefully, give rise to an extremely sensitive quantum tool. Some promising clues have been provided in this direction by numerical studies and experiments with cold atoms [3,4,5,6] but also with microwave cavities [7,8] where tunnelling signatures for processes that are forbidden by ray optics were observed.…”

Resonance- and Chaos-Assisted Tunneling in Mixed Regular-Chaotic Systems

“…Indeed, chaosassisted tunneling processes arise in a number of physical systems, e.g. in the ionization of resonantly driven hydrogen [7], in microwave or optical cavities [8,9], as well as in the effective pendulum dynamics describing tunneling experiments of cold atoms in optical lattices [10,11].…”

“…Indeed, chaosassisted tunneling processes arise in a number of physical systems, e.g. in the ionization of resonantly driven hydrogen [7], in microwave or optical cavities [8,9], as well as in the effective pendulum dynamics describing tunneling experiments of cold atoms in optical lattices [10,11].While the statistical properties of the chaos-assisted tunneling rates are well reproduced by a random matrix description of the chaotic part of the Hamiltonian [12], the formulation of a tractable and reliable semiclassical theory for the average tunneling rate is still an open problem. Promising progress in this direction was reported by Shudo and coworkers [13] who obtain a good quantitative reproduction of classically forbidden propagation processes in mixed systems by incorporating complex trajectories into the semiclassical propagator Their approach requires, however, the study of highly nontrivial structures in complex phase space, and cannot be straightforwardly connected to single coupling matrix elements between regular and chaotic states.…”

Tunable Fermi acceleration in a nondissipative driven magnetic billiard

“…If in addition, in the PAB, the circles are concentric, the angular momentum of the particle is a constant of motion and the phase space presents some regular structures, but if the circles are eccentric it is possible to observe the mechanism of FA. It is worth pointing out that the applied realization of the static annular billiard is reported theoretically [13] and experimentally [19]. The paper is organized as follows: In Sec.…”