Measurement of spectral functions of ultracold atoms in disordered potentials

We present a method allowing us to measure the spectral functions of non-interacting ultra-cold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by two orders of magnitude, we observe the crossover from the "quantum" perturbative regime of low disorder to the "classical" regime at higher disorder strength, and find an excellent agreement with numerical simulations. The experiment relies on the use of state-dependent disorder and the controlled transfer of atoms to create well-defined energy states. This opens new avenues for improved experimental investigations of three-dimensional Anderson localization.