Prethermal SPT phases and discrete time quasicrystals in a Rydberg array

The laboratory preparation of exotic quantum phases is a rapidly developing field with applications to quantum computing, simulation, and sensing. In this work, we discuss a proposal to program a neutral-atom quantum simulator to realize a symmetry-protected topological (SPT) state protected by multiple time-translation symmetries. We leverage recent advances in the study of prethermalization of quantum spin systems under strong, high-frequency quasiperiodic driving to engineer dynamics. Through extensive numerical simulations, we study the low temperature phase diagram of our model and implement time-dependent ramps of system parameters to demonstrate that the SPT phase can be prepared adiabatically. Importantly, the experimental techniques required to implement our proposal are already well-developed, making this scheme experimentally accessible. We also highlight extensions of this model as a route to experimentally realize two-dimensional Kitaev topological order exhibited by spin-liquid states.