Detailed structure of a localization phase diagram controlled by the interplay of driving and disorder

We report experimental study of the interplay between spatially quasiperiodic disorder and time-periodic driving using a 1D quasiperiodic cold-atom chain. We measure transport throughout a phase diagram with axes of drive amplitude and quasidisorder strength, and observe lobes of metallic phases bounded by quantum phase transitions arising from the competition of these two localizing mechanisms. While these observations are broadly consistent with the predictions of a high-drive-frequency theoretical model, we also observe clear quantitative departures from this model in the measured phase diagram, including drive-frequency dependent changes in localization behavior. We demonstrate, with the support of numerics, that these exotic measured features arise from higher-order terms beyond the high-frequency-drive approximation.