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Anderson localization is a universal phenomenon affecting non-interactingquantum particles in disorder. In three spatial dimensions it becomesparticularly interesting to study because of the presence of a quantum phasetransition from localized to extended states, predicted by P.W. Anderson in hisseminal work, taking place at a critical energy, the so-called mobility edge.The possible relation of the Anderson transition to the metal-insulatortransitions observed in materials has originated a flurry of theoreticalstudies during the past 50 years, and it is now possible to predict veryaccurately the mobility edge starting from models of the microscopic disorder.However, the experiments performed so far with photons, ultrasound andultracold atoms, while giving evidence of the transition, could not provide aprecise measurement of the mobility edge. In this work we are able to obtainsuch a measurement using an ultracold atomic system in a disordered specklepotential, thanks to a precise control of the system energy. We find that themobility edge is close to the mean disorder energy at small disorder strengths,while a clear effect of the spatial correlation of the disorder appears atlarger strengths. The precise knowledge of the disorder properties in oursystem offers now the opportunity for an unprecedented experiment-theorycomparison for 3D Anderson localization, which is also a necessary step tostart the exploration of novel regimes for many-body disordered systems.

Measurement of the mobility edge for 3D Anderson localization