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Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves: Theory and Experiment

Using a cold atomic gas exposed to laser pulses -- a realization of the chaotic quasiperiodic kicked rotor with three incommensurate frequencies -- we study experimentally and theoretically the Anderson metal-insulator transition in three dimensions. Sensitive measurements of the atomic wavefunction and the use of finite-size scaling techniques make it possible to unambiguously demonstrate the existence of a quantum phase transition and to measure its critical exponents. By taking proper account of systematic corrections to one-parameter scaling, we show the universality of the critical exponent $ν=1.59\pm0.01,$ which is found to be equal to the one previously computed for the Anderson model.