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Disorder can fundamentally modify the transport properties of a system. Astriking example is Anderson localization, suppressing transport due todestructive interference of propagation paths. In inhomogeneous many-bodysystems, not all particles are localized for finite-strength disorder, and thesystem can become partially diffusive. Unravelling the intricate signatures oflocalization from such observed diffusion is a long-standing problem. Here, weexperimentally study a degenerate, spin-polarized Fermi gas in a disorderpotential formed by an optical speckle pattern. We record the diffusion in thedisordered potential upon release from an external confining potential. Wecompare different methods to analyze the resulting density distributions,including a new method to capture particle dynamics by evaluatingabsorption-image statistics. Using standard observables, such as diffusionexponent and coefficient, localized fraction, or localization length, we findthat some show signatures for a transition to localization above a criticaldisorder strength, while others show a smooth crossover to a modified diffusionregime. In laterally displaced disorder, we spatially resolve differenttransport regimes simultaneously which allows us to extract the subdiffusionexponent expected for weak localization. Our work emphasizes that thetransition toward localization can be investigated by closely analyzing thesystem's diffusion, offering ways of revealing localization effects beyond thesignature of exponentially decaying density distribution.

What can we learn from diffusion about Anderson localization of a degenerate Fermi gas?