Experimental Realization of Discrete Time Quasi-Crystals

Floquet (periodically driven) systems can give rise to unique non-equilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: what other novel phases can manifest when the constraint of time periodicity is relaxed? In this study, we explore quantum systems subjected to a quasi-periodic drive. Leveraging a strongly interacting spin ensemble in diamond, we identify the emergence of long-lived discrete time quasi-crystals. Unlike conventional time crystals, time quasi-crystals exhibit robust sub-harmonic responses at multiple incommensurate frequencies. Furthermore, we show that the multi-frequency nature of the quasi-periodic drive allows for the formation of diverse patterns associated with different discrete time quasi-crystalline phases. Our findings demonstrate the existence of non-equilibrium phases in quasi-Floquet settings, significantly broadening the catalog of novel phenomena in driven many-body quantum systems.