Microwave experiments in the realm of fidelity

Abstract

In this review article, we will demonstrate the power of microwave experiments in the realm of fidelity also known as Loschmidt echoes. As the determination of the fidelity itself is experimentally tedious and error prone, we will introduce the scattering fidelity which under the conditions of chaotic systems and weak coupling approaches the fidelity itself. The main ingredient in fidelity investigations is the type and strength of a perturbation. The perturbations presented here will be both global and local boundary perturbations, as well as local perturber movements but also the change of coupling to the environment. All these perturbations will produce their own fidelity decay as a function of the perturbation strength, which will be discussed in this article.

Loschmidt echo and time reversal in complex systems

“…Among them, there are the experiments with microwave billiards, which played a very important role in the development of the field of quantum chaos and provided compelling evidence for many theoretically predicted decay regimes of the Loschmidt echo. Kuhl’s article [ 26 ] reviews the concept and applications of the scattering fidelity. The scattering fidelity is often used in microwave experiments as an echo measure, since, under the conditions of an underlying chaotic dynamics and a weak coupling of the measuring antenna, it approaches the ordinary fidelity.…”