In solid state physics, the study of the effects of disorder led to the discovery of a phase transition. For weak disorder, the solid is a conductor, whereas for strong disorder it becomes an insulator. This is known as the "Anderson transition" or as the "metal-insulator transition", and can be characterized by a critical exponent. It is theoretically predicted that this exponent's value is universal, i.e., that it is not determined by the microscopic details, but only by the symmetries of the Hamiltonian. The experimental realization of such a system in condensed matter is rather difficult. Decoherence effects cannot be neglected and affect critical exponent's value. To circumvent this phenomenon, we use cold atoms to experimentally realize a kicked rotor. The quantum dynamics of such a system are known to mimic those of the solid state problem. We hence test different sets of parameters controlling the statistical properties of the disorder, and show that the critical exponent is independent. We hereby prove the universality of the transition, and determine experimentally its universality class : the Gaussian Orthogonal Ensemble. We will then detail an important change in the experimental setup : the installation of a vertical standing wave, and of a time-of-flight velocimetric detection.
