Observation of continuous time crystals and quasi-crystals in spin gases

Continuous time crystals (CTCs) are a phase of matter characterized by spontaneous breaking of continuous time-translation symmetry. Recently, CTCs have garnered interest due to breakthroughs in experimental implementation. Here we report the experimental observation of CTCs in noble-gas nuclear spins and uncover previously unexplored dynamical phenomena. We observe that the CTCs manifest as persistent limit cycle oscillations of nuclear spins, with coherence times exceeding hours. Notably, these oscillations are robust against noise perturbations and exhibit random time phases upon repetitive realization, epitomizing continuous time-translation symmetry-breaking intrinsic to CTCs. Additionally, we observe a dynamical phase featuring quasi-periodic oscillations and random time phases, indicating the emergence of the continuous time quasi-crystals proposed by recent theories. By varying the feedback strength and magnetic gradient, we observe complex dynamical phase transitions between time crystal phases and chaotic regimes. This work broadens the catalog of phases of spin gases and unlocks opportunities in precision measurements.