Direct Observation of the Three-Dimensional Anderson Transition with Ultracold Atoms in a Disordered Potential

TL;DR

This study provides the first direct observation of the three-dimensional Anderson transition using ultracold atoms with a novel energy-resolved method, enabling precise measurement of the mobility edge and confirming theoretical predictions.

Contribution

The paper introduces a new energy-resolved experimental scheme that allows direct observation and precise measurement of the 3D Anderson transition in ultracold atoms, overcoming previous limitations.

Findings

Successful direct observation of the 3D Anderson transition.

Precise measurement of the mobility edge across various disorder strengths.

Excellent agreement with numerical predictions, resolving past discrepancies.

Abstract

Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling theory predicts a quantum phase transition at a critical energy, the mobility edge, separating localized from diffusive states and underpinning metal-insulator transitions in electronic systems. Despite decades of experimental efforts, a direct observation of this emblematic transition for matter waves has remained elusive. Previous attempts with ultracold atoms were hindered by strong and uncontrolled energy broadening, resulting in indirect, sometimes inaccurate, and model-dependent estimates of the mobility edge. Here we implement a novel energy-resolved scheme to prepare atomic matter waves with a narrow energy distribution and track their expansion dynamics over long timescales. This allows for a direct observation of the three-dimensional Anderson transition in a laser-speckle disordered potential, and for a precise measurement of the mobility edge that is independent of any underlying theoretical modeling. Our measurements show excellent agreement with state-of-the-art numerical predictions over a wide range of disorder strengths, resolving long-standing discrepancies between prior experiments and theory. Beyond the three-dimensional Anderson transition, our approach opens new avenues for quantitative investigations of quantum critical phenomena in spatially disordered systems, including the roles of dimensionality, symmetry class, and interactions.