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

Continuous time crystal (CTC) and quasi-crystal (CTQC) are two novel phases of matter characterized by the spontaneous breaking of continuous time-translation symmetry. To date, realizations of CTCs with periodic oscillations have been reported in only a few physical platforms, and their complex properties still require further exploration. Additionally, CTQCs, which feature quasi-periodic oscillations at multiple incommensurate frequencies, remain elusive. Here we report the experimental observation of CTC and CTQC signatures in noble-gas nuclear spins that interact nonlinearly with each other through feedback mechanisms. The observed limit cycle and quasi-periodic phases display persistent spin oscillations with coherence times extending beyond several hours. Notably, these oscillations are robust against noise perturbations and exhibit random time phases upon repetitive realization, epitomizing the continuous time-translation symmetry-breaking intrinsic to CTCs and CTQCs. As the feedback strength increases, the system undergoes a phase transition into a new phase characterized by chaotic oscillations, indicative of the ``melting" of time crystals. Interestingly, within certain feedback regimes, we even observe an unusual reverse phase transition from a chaotic phase back to time crystal phases. This work broadens the catalog of new phases of spin gas and unlocks opportunities in precision measurements, including multimode masers and tests of fundamental symmetries.