Quasi-Floquet prethermalization in a disordered spin ensemble in dimond

Floquet (periodic) driving has recently emerged as a powerful technique to control quantum systems via the so-called Floquet engineering (i.e. pulsed periodic driving). Such technique can help to prevent environment-induced decoherence and more recently, has enabled the study of novel quantum dynamical phenomena. However, a central challenge to stabilizing Floquet systems and observing such phenomena is the inevitable energy absorption from the driving fields. One potential solution--prethermalization--arises when the driving frequency is sufficiently larger than the system's local energy scale; the heating process is significantly suppressed and there exists a long-lived regime described by an effective static Hamiltonian. Despite this promise, the presence of long-range interactions and multiple driving frequencies may significantly alter the existence of prethermal behaviors. Crucially, there are two possible culprits for the breakdown of prethermalization: (1) The existence of long-range interactions may lead to a divergent local energy scale; (2) In the quasi-Floquet scenario with multiple driving frequencies, multi-photon processes may allow resonant absorption of energy from the drive. Here, we report the observation of prethermalization in a strongly interacting dipolar spin ensemble in diamond, where the interplay between the angular dependence and the long-range interaction helps to stabilize the system. More intriguingly, we extend our experimental observation to quasi-Floquet drivings with multiple incommensurate frequencies. In contrast to single-frequency drive, we observe that the existence of prethermalization is extremely sensitive to the smoothness of the applied fields. To complement our experimental observation, we also present a theoretical understanding of the energy absorption under quasi-periodic drive. Our results open the door to robust Floquet engineering and experimental investigation of non-equilibrium phenomena with multi-frequency drive.