  We study experimentally a quantum kicked rotor with broken parity symmetry,
supporting a ratchet effect due to the presence of a classical accelerator
mode. We show that the short-time dynamics is very well described by the
classical dynamics, characterized by a strongly asymmetric momentum
distribution with directed motion on one side, and an anomalous diffusion on
the other. At longer times, quantum effects lead to dynamical localization,
causing an asymptotic resymmetrization of the wave function.
