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Floquet (periodic) driving has recently emerged as a powerful technique forengineering quantum systems and realizing non-equilibrium phases of matter. Acentral challenge to stabilizing quantum phenomena in such systems is the needto prevent energy absorption from the driving field. Fortunately, when thefrequency of the drive is significantly larger than the local energy scales ofthe many-body system, energy absorption is suppressed. The existence of thisso-called prethermal regime depends sensitively on the range of interactionsand the presence of multiple driving frequencies. Here, we report theobservation of Floquet prethermalization in a strongly interacting dipolar spinensemble in diamond, where the angular dependence of the dipolar coupling helpsto mitigate the long-ranged nature of the interaction. Moreover, we extend ourexperimental observation to quasi-Floquet drives with multiple incommensuratefrequencies. In contrast to a single-frequency drive, we find that theexistence of prethermalization is extremely sensitive to the smoothness of theapplied field. Our results open the door to stabilizing and characterizingnon-equilibrium phenomena in quasi-periodically driven systems.

Quasi-Floquet prethermalization in a disordered dipolar spin ensemble in diamond