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 transitions1, 2. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter3, 4, 5, 6; for example, the interplay between periodic driving, disorder and strong interactions has been predicted to result in exotic ‘time-crystalline’ phases7, in which a system exhibits temporal correlations at integer multiples of the fundamental driving period, breaking the discrete time-translational symmetry of the underlying drive8, 9, 10, 11, 12. 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 temperature13, 14, 15. 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 thermalization16, 17. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems18, 19, 20.
At a glance
- A study of locking phenomena in oscillators. Proc. IRE 34, 351–357 (1946)
- Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993) &
- Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015) et al.
- Experimental observation of a generalized Gibbs ensemble. Science 348, 207–211 (2015) et al.
- Many-body localization in a quantum simulator with programmable random disorder. Nat. Phys. 12, 907–911 (2016) et al.
- Quantum thermalization through entanglement in an isolated many-body system. Science 353, 794–800 (2016) et al.
- Quantum time crystals. Phys. Rev. Lett. 109, 160401 (2012)
- Modeling spontaneous breaking of time-translation symmetry. Phys. Rev. A 91, 033617 (2015)
- Phase structure of driven quantum systems. Phys. Rev. Lett. 116, 250401 (2016) , , &
- Floquet time crystals. Phys. Rev. Lett. 117, 090402 (2016) , &
- Absolute stability and spatiotemporal long-range order in Floquet systems. Phys. Rev. B 94, 085112 (2016) , &
- Discrete time crystals: rigidity, criticality, and realizations. Phys. Rev. Lett. 118, 030401 (2017) , , &
- Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science 314, 281–285 (2006) et al.
- Universal dynamical decoupling of a single solid-state spin from a spin bath. Science 330, 60–63 (2010) , , , &
- The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1–45 (2013) et al.
- Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958)
- https://arxiv.org/abs/1609.08216 (2016) et al. Critical thermalization of a disordered dipolar spin system in diamond. Preprint at
- Spin self-rephasing and very long coherence times in a trapped atomic ensemble. Phys. Rev. Lett. 105, 020401 (2010) et al.
- Many-body protected entanglement generation in interacting spin systems. Phys. Rev. A 77, 052305 (2008) , , , &
- Quantum correlation in disordered spin systems: applications to magnetic sensing. Phys. Rev. A 80, 032311 (2009) &
- Approach to high-resolution NMR in solids. Phys. Rev. Lett. 20, 180–182 (1968) , &
- Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states. Ann. Phys. 321, 1126–1205 (2006) , &
- Many-body localization and thermalization in quantum statistical mechanics. Annu. Rev. Condens. Matter Phys. 6, 15–38 (2015) &
- Exponentially slow heating in periodically driven many-body systems. Phys. Rev. Lett. 115, 256803 (2015) , &
- Impossibility of spontaneously rotating time crystals: a no-go theorem. Phys. Rev. Lett. 111, 070402 (2013)
- Absence of quantum time crystals. Phys. Rev. Lett. 114, 251603 (2015) &
- https://arxiv.org/abs/1607.05277 (2016) , & Pre-thermal time crystals and Floquet topological phases without disorder. Preprint at
- Phys. Rev. Lett. (in the press) et al. Depolarization dynamics in a strongly interacting solid-state spin ensemble.
- Phase structure of one-dimensional interacting Floquet systems. II. Symmetry-broken phases. Phys. Rev. B 93, 245146 (2016) &
- Period three implies chaos. Am. Math. Mon. 82, 985–992 (1975) &
- Many-body localization in dipolar systems. Phys. Rev. Lett. 113, 243002 (2014) et al.
Extended data figures and tables
Extended Data Figures
- Extended Data Figure 1: Effect of rotary echo sequence. (227 KB)
a, Experimental sequence: during the interaction interval τ1, the phase of the microwave driving along is inverted after τ1/2. b, Comparison of time traces of P(nT), measured at even (green) and odd (blue) integer multiples of T, in the presence (left) and absence (right) of an rotary echo sequence at similar τ1 and θ (left, τ1 = 379 ns, θ = 0.979π; right, τ1 = 384 ns, θ = 0.974π). The rotary echo leads to more pronounced 2T-periodic oscillations at long time. The microwave frequencies used in the rotary echo sequence are Ωx = 2π × 52.9 MHz and Ωy = 2π × 42.3 MHz.