Observation of a critical prethermal discrete time crystal created by two-frequency driving

Abstract: We report the observation of long-lived Floquet prethermal discrete time crystalline (PDTC) order in a three-dimensional position-disordered lattice of interacting dipolar-coupled 13C nuclei in diamond at room temperature. We demonstrate a novel strategy of "two-frequency" driving, involving an interleaved application of slow and fast drives that simultaneously prethermalize the spins with an emergent quasi-conserved magnetization along the x-axis, while enabling continuous and highly resolved observation of their dynamic evolution when periodically kicked away from x. The PDTC order manifests itself in a robust period doubling response of this drive-induced quasi-conserved spin magnetization interchanging between x and -x; our experiments allow a unique means to study the formation and melting of PDTC order. We obtain movies of the time-crystalline response with a clarity and throughput orders of magnitude greater than previous experiments. Parametric control over the drive frequencies allows us to reach PDTC lifetimes up to 396 Floquet cycles which we measure in a single-shot experiment. Such rapid measurement enables detailed characterization of the entire PDTC phase diagram, rigidity and lifetime, informing on the role of prethermalization towards stabilizing the DTC response. The two-frequency drive approach represents the simplest generalization of DTCs to multi-frequency drives; it expands the toolkit for realizing and investigating long-lived non-equilibrium phases of matter stabilized by emergent quasi-conservation laws.