title: Observation of discrete time-crystalline order in a disordered dipolar many-body system.
abstract: Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. Out-of-equilibrium systems can display a rich variety of phenomena, including self-organized synchronization and dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter; for example, the interplay between periodic driving, disorder and strong interactions has been predicted to result in exotic 'time-crystalline' phases, in which a system exhibits temporal correlations at integer multiples of the fundamental driving period, breaking the discrete time-translational symmetry of the underlying drive. Here we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of about one million dipolar spin impurities in diamond at room temperature. We observe long-lived temporal correlations, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions. This order is remarkably stable to perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Soonwon
authors.initials: S
authors.lastname: Choi
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.|School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Joonhee
authors.initials: J
authors.lastname: Choi
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Renate
authors.initials: R
authors.lastname: Landig
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Georg
authors.initials: G
authors.lastname: Kucsko
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Hengyun
authors.initials: H
authors.lastname: Zhou
authors.affiliation: Research Centre for Knowledge Communities, University of Tsukuba, Tsukuba, Ibaraki 305-8550, Japan.
authors.forename: Junichi
authors.initials: J
authors.lastname: Isoya
authors.affiliation: Institut für Quantenoptik, Universität Ulm, 89081 Ulm, Germany.
authors.forename: Fedor
authors.initials: F
authors.lastname: Jelezko
authors.affiliation: Takasaki Advanced Radiation Research Institute, National Institutes for Quantum and Radiological Science and Technology, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan.
authors.forename: Shinobu
authors.initials: S
authors.lastname: Onoda
authors.affiliation: Sumitomo Electric Industries Ltd., Itami, Hyougo, 664-0016, Japan.
authors.forename: Hitoshi
authors.initials: H
authors.lastname: Sumiya
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Vedika
authors.initials: V
authors.lastname: Khemani
authors.affiliation: Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Curt
authors.initials: C
authors.lastname: von Keyserlingk
authors.affiliation: Department of Physics, University of California Berkeley, Berkeley, California 94720, USA.
authors.forename: Norman Y
authors.initials: NY
authors.lastname: Yao
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Eugene
authors.initials: E
authors.lastname: Demler
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Mikhail D
authors.initials: MD
authors.lastname: Lukin