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

Nature volume 543, pages 221–225 (2017)Cite this article

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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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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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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.

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Author notes

  1. Soonwon Choi, Joonhee Choi and Renate Landig: These authors contributed equally to this work.

Authors and Affiliations

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

    Joonhee Choi

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

    Junichi Isoya

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

    Fedor Jelezko

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

    Shinobu Onoda

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

    Hitoshi Sumiya

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

    Curt von Keyserlingk

  8. Department of Physics, University of California Berkeley, Berkeley, 94720, California, USA

    Norman Y. Yao

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  1. Soonwon Choi
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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.

Corresponding author

Correspondence to Mikhail D. Lukin.

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Competing interests

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). https://doi.org/10.1038/nature21426

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