Observation of Discrete Time Quasi-Crystalline Order in a Strongly Interacting Spin Ensemble in Diamond

Floquet driven systems offer a versatile toolkit for exploring non-equilibrium phases of matter. Introducing a single-frequency drive allows the realization of a novel phase of matter dubbed a 'discrete time crystal' (DTC), characterized by a persistent oscillatory response with a subharmonic frequency. More intriguing phenomena emerges as one replaces the single frequency drive with a multi-frequency one with incommensurate frequencies. In this study, we delve into the realm of discrete time quasicrystals (DTQC) utilizing a strongly interacting spin ensemble in diamond. When subjected to a quasi-periodic drive, the DTQC exhibits multiple subharmonic responses at various frequencies. Notably, we demonstrate the robustness of these responses against perturbation, protected by the many-body interactions within the spin ensemble. To quantify this rigidity, we map out the phase diagram of the DTQC by manipulating the interaction strength and the perturbation magnitude. Our findings significantly expand the scope of simulating and characterizing many-body phenomena in quasi-periodically driven systems.