Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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

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

Subjects

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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

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.

References

  1. Adler, R. A study of locking phenomena in oscillators. Proc. IRE 34, 351–357 (1946)

    Article  Google Scholar 

  2. Cross, M. C. & Hohenberg, P. C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993)

    Article  CAS  ADS  Google Scholar 

  3. Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015)

    Article  CAS  ADS  MathSciNet  Google Scholar 

  4. Langen, T. et al. Experimental observation of a generalized Gibbs ensemble. Science 348, 207–211 (2015)

    Article  CAS  ADS  MathSciNet  Google Scholar 

  5. Smith, J. et al. Many-body localization in a quantum simulator with programmable random disorder. Nat. Phys. 12, 907–911 (2016)

    Article  CAS  Google Scholar 

  6. Kaufman, A. M. et al. Quantum thermalization through entanglement in an isolated many-body system. Science 353, 794–800 (2016)

    Article  CAS  ADS  Google Scholar 

  7. Wilczek, F. Quantum time crystals. Phys. Rev. Lett. 109, 160401 (2012)

    Article  ADS  Google Scholar 

  8. Sacha, K. Modeling spontaneous breaking of time-translation symmetry. Phys. Rev. A 91, 033617 (2015)

    Article  ADS  Google Scholar 

  9. Khemani, V., Lazarides, A., Moessner, R. & Sondhi, S. L. Phase structure of driven quantum systems. Phys. Rev. Lett. 116, 250401 (2016)

    Article  ADS  Google Scholar 

  10. Else, D. V., Bauer, B. & Nayak, C. Floquet time crystals. Phys. Rev. Lett. 117, 090402 (2016)

    Article  ADS  Google Scholar 

  11. von Keyserlingk, C., Khemani, V. & Sondhi, S. Absolute stability and spatiotemporal long-range order in Floquet systems. Phys. Rev. B 94, 085112 (2016)

    Article  ADS  Google Scholar 

  12. Yao, N. Y., Potter, A. C., Potirniche, I.-D. & Vishwanath, A. Discrete time crystals: rigidity, criticality, and realizations. Phys. Rev. Lett. 118, 030401 (2017)

    Article  CAS  ADS  MathSciNet  Google Scholar 

  13. Childress, L. et al. Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science 314, 281–285 (2006)

    Article  CAS  ADS  Google Scholar 

  14. de Lange, G., Wang, Z. H., Ristè, D., Dobrovitski, V. V. & Hanson, R. Universal dynamical decoupling of a single solid-state spin from a spin bath. Science 330, 60–63 (2010)

    Article  CAS  ADS  Google Scholar 

  15. Doherty, M. W. et al. The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1–45 (2013)

    Article  CAS  ADS  Google Scholar 

  16. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958)

    Article  CAS  ADS  Google Scholar 

  17. Kucsko, G. et al. Critical thermalization of a disordered dipolar spin system in diamond. Preprint at https://arxiv.org/abs/1609.08216 (2016)

  18. Deutsch, C. et al. Spin self-rephasing and very long coherence times in a trapped atomic ensemble. Phys. Rev. Lett. 105, 020401 (2010)

    Article  CAS  ADS  Google Scholar 

  19. Rey, A. M., Jiang, L., Fleischhauer, M., Demler, E. & Lukin, M. D. Many-body protected entanglement generation in interacting spin systems. Phys. Rev. A 77, 052305 (2008)

    Article  ADS  Google Scholar 

  20. Cappellaro, P. & Lukin, M. D. Quantum correlation in disordered spin systems: applications to magnetic sensing. Phys. Rev. A 80, 032311 (2009)

    Article  ADS  Google Scholar 

  21. Waugh, J., Huber, L. & Haeberlen, U. Approach to high-resolution NMR in solids. Phys. Rev. Lett. 20, 180–182 (1968)

    Article  CAS  ADS  Google Scholar 

  22. Basko, D., Aleiner, I. & Altshuler, B. Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states. Ann. Phys. 321, 1126–1205 (2006)

    Article  CAS  ADS  Google Scholar 

  23. Nandkishore, R. & Huse, D. A. Many-body localization and thermalization in quantum statistical mechanics. Annu. Rev. Condens. Matter Phys. 6, 15–38 (2015)

    Article  ADS  Google Scholar 

  24. Abanin, D. A., De Roeck, W. & Huveneers, F. Exponentially slow heating in periodically driven many-body systems. Phys. Rev. Lett. 115, 256803 (2015)

    Article  ADS  Google Scholar 

  25. Bruno, P. Impossibility of spontaneously rotating time crystals: a no-go theorem. Phys. Rev. Lett. 111, 070402 (2013)

    Article  ADS  Google Scholar 

  26. Watanabe, H. & Oshikawa, M. Absence of quantum time crystals. Phys. Rev. Lett. 114, 251603 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  27. Else, D. V., Bauer, B. & Nayak, C. Pre-thermal time crystals and Floquet topological phases without disorder. Preprint at https://arxiv.org/abs/1607.05277 (2016)

  28. Choi, J. et al. Depolarization dynamics in a strongly interacting solid-state spin ensemble. Phys. Rev. Lett. (in the press)

  29. von Keyserlingk, C. W. & Sondhi, S. L. Phase structure of one-dimensional interacting Floquet systems. II. Symmetry-broken phases. Phys. Rev. B 93, 245146 (2016)

    Article  ADS  Google Scholar 

  30. Li, T.-Y. & Yorke, J. A. Period three implies chaos. Am. Math. Mon. 82, 985–992 (1975)

    Article  MathSciNet  Google Scholar 

  31. Yao, N. Y. et al. Many-body localization in dipolar systems. Phys. Rev. Lett. 113, 243002 (2014)

    Article  CAS  ADS  Google Scholar 

Download references

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

  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

Authors
  1. Soonwon Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joonhee Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Renate Landig
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Georg Kucsko
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hengyun Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Junichi Isoya
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Fedor Jelezko
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Shinobu Onoda
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Hitoshi Sumiya
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Vedika Khemani
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Curt von Keyserlingk
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Norman Y. Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Eugene Demler
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Mikhail D. Lukin
    View author publications

    You can also search for this author in PubMed Google Scholar

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.

Ethics declarations

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.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature21426

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing