Driving versus disorder: interplay of dynamic localization and Aubry-André localization in a cold atom quasicrystal

We report the experimental study of an ultracold atomic gas in a bichromatic optical lattice subjected to both dipolar driving and quasi-disorder. We measure a rich localization phase diagram as a function of drive amplitude and quasi-disorder strength which arises due to the competition between these two localizing effects. The observed quantum phase transition displays multiple lobes which can be understood as arising from a competition between quasi-disorder and effective tunneling energy, but also comprises several features which are not present in this first-order theory. We argue, with the support of numerics, that these exotic features arise from higher-order terms beyond the high-frequency-drive approximation.