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Observation of discrete time-crystalline order in a disordered dipolar many-body system


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.

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Figure 1: Experimental set-up and observation of discrete time-crystalline order.
Figure 2: Long-time behaviour of discrete time-crystalline order.
Figure 3: Phase diagram and transition.
Figure 4: Z3 discrete time-crystalline order.

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We thank D. A. Huse, S. L. Sondhi, A. Vishwanath and M. Zaletel for discussions, and N. P. De Leon and P. C. Maurer for fabricating the diamond nanobeam and experimental help. This work was supported in part by CUA, NSSEFF, ARO MURI, Moore Foundation, Harvard Society of Fellows, Princeton Center for Theoretical Science, Miller Institute for Basic Research in Science, Kwanjeong Educational Foundation, Samsung Fellowship, Purcell Fellowship, NSF PHY-1506284, NSF DMR-1308435, Japan Society for the Promotion of Science KAKENHI (No. 26246001), LDRD Program of LBNL under US DOE Contract No. DE-AC02-05CH11231, EU (FP7, Horizons 2020, ERC), DFG, SNF, Volkswagenstiftung and BMBF.

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Authors and Affiliations



S.C. and M.D.L. developed the idea for the study. J.C., R.L. and G.K. designed and conducted the experiment. H.S., S.O., J.I. and F.J. fabricated the sample. S.C., H.Z., V.K., C.v.K., N.Y.Y. and E.D. conducted the theoretical analysis. All authors discussed the results and contributed to the manuscript.

Corresponding author

Correspondence to Mikhail D. Lukin.

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The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks D. A. Huse and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 Effect of rotary echo sequence.

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.

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Choi, S., Choi, J., Landig, R. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).

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