Quasi-Floquet engineering of a dipolar many-body spin system in diamond

Floquet (periodic) driving has recently emerged as a powerful technique for engineering quantum systems and realizing non-equilibrium phases of matter. Even richer phenomena can arise in "quasi-Floquet" settings, where a single time-translation symmetry is replaced by multiple time-translation symmetries. Here, we present our recent results on the observation of quasi-Floquet prethermalization in a strongly-interacting nitrogen-vacancy (NV) spin ensemble in diamond. In contrast to a single-frequency (Floquet) drive, we find that the existence of prethermalization is extremely sensitive to the smoothness of the applied field. Moreover, using quasi-Floquet engineering, we realize discrete time quasi-crystalline order which is fundamentally distinct from those realizable in periodically driven (Floquet) systems. Our results open the door to stabilizing and characterizing many-body phenomena in quasi-periodically driven systems.