Letter

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

Received:
Accepted:
Published online:

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 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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Acknowledgements

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.

Author information

Author notes

    • Soonwon Choi
    • , Joonhee Choi
    •  & Renate Landig

    These authors contributed equally to this work.

Affiliations

  1. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    • Soonwon Choi
    • , Joonhee Choi
    • , Renate Landig
    • , Georg Kucsko
    • , Hengyun Zhou
    • , Vedika Khemani
    • , Eugene Demler
    •  & Mikhail D. Lukin
  2. School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

    • Joonhee Choi
  3. Research Centre for Knowledge Communities, University of Tsukuba, Tsukuba, Ibaraki 305-8550, Japan

    • Junichi Isoya
  4. Institut für Quantenoptik and Center for Integrated Quantum Science and Technology, Universität Ulm, 89081 Ulm, Germany

    • Fedor Jelezko
  5. Takasaki Advanced Radiation Research Institute, National Institutes for Quantum and Radiological Science and Technology, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan

    • Shinobu Onoda
  6. Sumitomo Electric Industries Ltd, Itami, Hyougo 664-0016, Japan

    • Hitoshi Sumiya
  7. Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA

    • Curt von Keyserlingk
  8. Department of Physics, University of California Berkeley, Berkeley, California 94720, USA

    • Norman Y. Yao

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Contributions

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.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Mikhail D. Lukin.

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

Extended data figures

  1. 1.

    Effect of rotary echo sequence.

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