Experimental observation of a time rondeau crystal

Conventional phases of matter can be characterized by the symmetries they break, one example being water ice whose crystalline structure breaks the continuous translation symmetry of space. Recently, breaking of time-translation symmetry was observed in non-equilibrium systems, producing so-called time crystals. Here we investigate different kinds of partial temporal ordering, stabilized by non-periodic yet structured drives, which we call the rondeau order. Using carbon-13 nuclear spins in diamond as a quantum simulator, we use microwave driving fields to create tunable short-time disorder in a system exhibiting long-time stroboscopic order. Our spin control architecture allows us to implement a family of driving fields including periodic, aperiodic and structured random drives. We use a high-throughput read-out scheme to continuously observe the spin polarization and its rondeau order, with controllable lifetimes exceeding 4 s. Using degrees of freedom associated with the short-time temporal disorder of rondeau order, we demonstrate the capacity to encode information in the response of observables. Our work broadens the landscape of observed non-equilibrium temporal order, and raises the prospect for the potential applications of driven quantum matter.