Abstract
We discuss a general useful theoretical framework to study dynamical localization in ultracold atomic systems confined in periodically shaken optical lattices. Our theory allows to understand some limitations of the usual approach concerning prototypical $\ensuremath{\delta}$-kicked systems, as well as to explain the experimental results for which finite-time effects cannot be neglected. Specifically, we predict that the strength of dynamical localization reaches a maximum as a function of the width of the pulsatile modulation, whenever its amplitude and period satisfy a given relationship. Additionally, we describe a quite simple scenario for the quantum suppression of classical diffusion, which is confirmed by extensive numerical simulations: The activation of Heisenberg's uncertainty principle giving rise to a drastic reduction of the quantum momentum dispersion if, and only if, the classical dynamics is sufficiently chaotic.
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