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 closely-spaced pairs of pulses in an optical lattice. The experiments show the interplay between fully coherent quantum dynamics and a novel momentum-diffusion regime: 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. Analytical formulae are presented and, with quantum localization, are used to analyse the experiments.