44. Critical prethermal discrete time crystal created by two-frequency driving

W. Beatrez†, C. Fleckenstein†, A. Pillai, E. Sanchez, A. Akkiraju, J. Alcala, S. Conti, P. Reshetikhin, E. Druga, M. Bukov*, A. Ajoy* [PDF]
arXiv:2201.02162 — Nature Physics 19, 407 (2023)
Watch the formation and melting of a time-crystal: [Video 1] , [Video 2] , [Video 3] .

Abstract:
Discrete time crystals are non-equilibrium many-body phases of matter characterized by spontaneously broken discrete time-translation symmetry under periodic driving. At sufficiently high driving frequencies, the system enters the Floquet prethermalization regime, in which the periodically driven many-body state has a lifetime vastly exceeding the intrinsic decay time of the system. Here, we report the observation of long-lived prethermal discrete time-crystalline order in a three-dimensional (3D) lattice of 13C nuclei in diamond at room temperature. We demonstrate a two-frequency driving protocol, involving an interleaved application of slow and fast drives that simultaneously prethermalize the spins with an emergent quasi-conserved magnetization along the x̂ axis. This enables continuous and highly resolved observation of their dynamic evolution. We obtain videos 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 time-crystal lifetimes of up to 396 Floquet cycles, which we measure in a single-shot experiment. Such rapid measurement enables detailed characterization of the entire phase diagram, highlighting the role of prethermalization in stabilizing the time-crystal response. The two-frequency drive approach expands the toolkit for investigating non-equilibrium phases of matter stabilized by emergent quasi-conservation laws.