  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.
