Quantum diffusion in the quasiperiodic kicked rotor

– We study the mechanisms responsible for quantum diffusion in the quasiperiodic kicked rotor. We report experimental measurements of the diffusion constant on the atomic version of the system and develop a theoretical approach (based on the Floquet theorem) explaining the observations, especially the “sub-Fourier” character of the resonances observed in the vicinity of exact periodicity, i.e. the ability of the system to distinguish two neighboring driving frequencies in a time shorter than the inverse of the difference of the two frequencies. Quantum chaos is the study of quantum systems whose classical limit is chaotic. A major challenge of quantum chaos is to understand the mechanisms that make quantum chaos different from classical chaos. An important difference between classical and quantum systems is the existence in the latter of interferences between various paths. At long times, a large number of complicated trajectories interfere. One could expect the contributions of the various paths to have uncorrelated phases, so that the interference terms vanish in the average after some time, implying that quantum and classical transport should be identical. This simple expectation is however too naive, because phases of the various paths are actually correlated; this is for example the case for the kicked rotor. The quantum kicked rotor has been extensively studied experimentally in recent years [1–4]. In its atomic version it consists of a cloud of laser-cooled atoms exposed to short pulses of a far detuned, standing laser wave, corresponding to the Hamiltonian (for the external motion of the atoms)