Probing Localization in Absorbing Systems via Loschmidt Echos

TL;DR

This paper investigates Anderson localization in absorbing waveguides by analyzing Loschmidt echoes, revealing that the decay is governed by the inverse participation number, with theory matching microwave cavity experiments.

Contribution

It introduces a novel approach to probe localization in absorbing systems using Loschmidt echo dynamics and provides a theoretical model that aligns with experimental results.

Findings

Inverse participation number controls echo decay in localized systems

Loschmidt echo decay differs from Gaussian decay in diffusive systems

Theory matches experimental measurements in microwave cavities

Abstract

We measure Anderson localization in quasi-one-dimensional waveguides in the presence of absorption by analyzing the echo dynamics due to small perturbations. We specifically show that the inverse participation number of localized modes dictates the decay of the Loschmidt echo, differing from the Gaussian decay expected for diffusive or chaotic systems. Our theory, based on a random matrix modeling, agrees perfectly with scattering echo measurements on a quasi one-dimensional microwave cavity filled with randomly distributed scatterers.