Critical State of the Anderson Transition: Between a Metal and an Insulator

Using a three-frequency one-dimensional kicked rotor experimentally realized with a cold atomic gas, we study the transport properties at the critical point of the metal-insulator Anderson transition. We accurately measure the time evolution of an initially localized wave packet and show that it displays at the critical point a scaling invariance characteristic of this second-order phase transition. The shape of the momentum distribution at the critical point is found to be in excellent agreement with the analytical form deduced from the self-consistent theory of localization.