Atoms in double-delta-kicked periodic potentials: chaos with long-range correlations

We report an experimental and theoretical study of the dynamics of cold atoms subjected to pairs of closely spaced pulses in an optical lattice. For all previously studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2- or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged global correlations, between all kick pairs, which control transport through trapping regions in phase space. Correlations are studied in the classical regime, but the diffusive behavior observed in experiment depends on the quantum dynamical localization.