Exploring quasicrystal dynamics with degenerate strontium

Ultracold atoms in 1D bichromatic optical lattices realize the Aubry-André-Harper model, enabling the dynamical study of localization, pseudo-disorder, and quasicrystals. We report recent results on the coherent control of Aubry-André localization by phasonic modulation, and the experimental realization of the kicked Aubry-André-Harper (kAAH) model via periodic pulsing of the secondary lattice. In the latter case, we explore the global phase diagram of the kAAH model using a Floquet apodization technique. We discuss extensions to these studies, including the implementation of time-reversed evolution in the Aubry-Andre model and the investigation of the interplay between disorder-induced localization and dynamic localization. Separately, we discuss planned upgrades and future directions including a scheme for phase-stabilized 2D optical lattices with tunable geometry.