  Floquet (periodic) driving has recently emerged as a powerful technique for
engineering quantum systems and realizing non-equilibrium phases of matter. A
central challenge to stabilizing quantum phenomena in such systems is the need
to prevent energy absorption from the driving field. Fortunately, when the
frequency of the drive is significantly larger than the local energy scales of
the many-body system, energy absorption is suppressed. The existence of this
so-called prethermal regime depends sensitively on the range of interactions
and the presence of multiple driving frequencies. Here, we report the
observation of Floquet prethermalization in a strongly interacting dipolar spin
ensemble in diamond, where the angular dependence of the dipolar coupling helps
to mitigate the long-ranged nature of the interaction. Moreover, we extend our
experimental observation to quasi-Floquet drives with multiple incommensurate
frequencies. In contrast to a single-frequency drive, we find that the
existence of prethermalization is extremely sensitive to the smoothness of the
applied field. Our results open the door to stabilizing and characterizing
non-equilibrium phenomena in quasi-periodically driven systems.
