Measurement of the mobility edge for 3D Anderson localization

TL;DR

This study precisely measures the mobility edge in 3D Anderson localization using ultracold atoms, revealing its dependence on disorder strength and correlations, enabling detailed comparison with theoretical models.

Contribution

The paper presents the first precise experimental measurement of the mobility edge in 3D Anderson localization with ultracold atoms, improving understanding of disorder effects.

Findings

Mobility edge is near the mean disorder energy at low disorder strengths.

Spatial correlations of disorder significantly affect the mobility edge at higher disorder strengths.

The results enable detailed comparison between experiment and theory for 3D Anderson localization.

Abstract

Anderson localization is a universal phenomenon affecting non-interacting quantum particles in disorder. In three spatial dimensions it becomes particularly interesting to study because of the presence of a quantum phase transition from localized to extended states, predicted by P.W. Anderson in his seminal work, taking place at a critical energy, the so-called mobility edge. The possible relation of the Anderson transition to the metal-insulator transitions observed in materials has originated a flurry of theoretical studies during the past 50 years, and it is now possible to predict very accurately the mobility edge starting from models of the microscopic disorder. However, the experiments performed so far with photons, ultrasound and ultracold atoms, while giving evidence of the transition, could not provide a precise measurement of the mobility edge. In this work we are able to obtain such a measurement using an ultracold atomic system in a disordered speckle potential, thanks to a precise control of the system energy. We find that the mobility edge is close to the mean disorder energy at small disorder strengths, while a clear effect of the spatial correlation of the disorder appears at larger strengths. The precise knowledge of the disorder properties in our system offers now the opportunity for an unprecedented experiment-theory comparison for 3D Anderson localization, which is also a necessary step to start the exploration of novel regimes for many-body disordered systems.