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.

AC Josephson effect between two superfluid time crystals

Abstract

Quantum time crystals are systems characterized by spontaneously emerging periodic order in the time domain1. While originally a phase of broken time translation symmetry was a mere speculation2, a wide range of time crystals has been reported3,4,5. However, the dynamics and interactions between such systems have not been investigated experimentally. Here we study two adjacent quantum time crystals realized by two magnon condensates in superfluid 3He-B. We observe an exchange of magnons between the time crystals leading to opposite-phase oscillations in their populations—a signature of the AC Josephson effect6—while the defining periodic motion remains phase coherent throughout the experiment. Our results demonstrate that time crystals obey the general dynamics of quantum mechanics and offer a basis to further investigate the fundamental properties of these phases, opening pathways for possible applications in developing fields, such as quantum information processing.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Fig. 1: Experimental set-up.
Fig. 2: Time crystal AC Josephson effect.
Fig. 3: Josephson effect analysis.

Data availability

The data that support the findings of this study are available from ref. 39.

Code availability

The code used to generate the simulations and guidance in their use can be accessed from the corresponding author S.A. upon reasonable request.

References

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

    Article  Google Scholar 

  2. Ball, P. In search of time crystals. Physics World 31, 29–33 (2018).

    Article  Google Scholar 

  3. Sacha, K. & Zakrzewski, J. Time crystals: a review. Rep. Prog. Phys. 81, 016401 (2017).

    Article  Google Scholar 

  4. Else, D. V., Monroe, C., Nayak, C. & Yao, N. Y. Discrete time crystals. Annu. Rev. Condens. Matter Phys. 11, 467–499 (2020).

    Article  Google Scholar 

  5. Yao, N., Nayak, C., Balents, L. & Zaletel, M. Classical discrete time crystals. Nat. Phys. 16, 438–447 (2020).

    Article  CAS  Google Scholar 

  6. Josephson, B. Possible new effect in superconducting tunneling. Phys. Lett. 1, 251–253 (1962).

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Autti, S., Eltsov, V. B. & Volovik, G. E. Observation of a time quasicrystal and its transition to a superfluid time crystal. Phys. Rev. Lett. 120, 215301 (2018).

    Article  CAS  Google Scholar 

  9. Bunkov, Y. M. & Volovik, G. E. Novel Superfluids Vol. 1 (Oxford University Press, 2013).

  10. Borovik-Romanov, A. S. et al. Observation of a spin-current analog of the Josephson effect. JETP Lett. 47, 1033–1037 (1988).

    Google Scholar 

  11. Levy, S., Lahoud, E., Shomroni, I. & Steinhauer, J. The a.c. and d.c. Josephson effects in a Bose–Einstein condensate. Nature 449, 579–583 (2007).

    Article  CAS  Google Scholar 

  12. Valtolina, G. et al. Josephson effect in fermionic superfluids across the BEC-BCS crossover. Science 350, 1505–1508 (2015).

    Article  CAS  Google Scholar 

  13. Abbarchi, M. et al. Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons. Nat. Phys. 9, 275–279 (2013).

    Article  CAS  Google Scholar 

  14. Troncoso, R. E. & Núñez, Á. S. Josephson effects in a Bose-Einstein condensate of magnons. Ann. Phys. 346, 182 – 194 (2014).

    Article  Google Scholar 

  15. Nakata, K., van Hoogdalem, K., Simon, P. & Loss, D. Josephson and persistent spin currents in Bose-Einstein condensates of magnons. Phys. Rev. B 90, 144419 (2014).

    Article  Google Scholar 

  16. Bunkov, Y. M., Fisher, S. N., Guénault, A. M. & Pickett, G. R. Persistent spin precession in 3He-B in the regime of vanishing quasiparticle density. Phys. Rev. Lett. 69, 3092–3095 (1992).

    Article  CAS  Google Scholar 

  17. Fisher, S. et al. Thirty-minute coherence in free induction decay signals in superfluid 3He-B. J. Low Temp. Phys. 121, 303–308 (2000).

    Article  CAS  Google Scholar 

  18. Borovik-Romanov, A. S., Bun’kov, Y. M., Dmitriev, V. V. & Mukharskii, Y. M. Long-lived induction signal in superfluid 3He-B. JETP Lett. 40, 1033–1037 (1984).

    Google Scholar 

  19. Bunkov, Y. M. & Volovik, G. E. Magnon Bose–Einstein condensation and spin superfluidity. J. Phys. Condens. Matter 22, 164210 (2010).

    Article  Google Scholar 

  20. Bozhko, D. et al. Bogoliubov waves and distant transport of magnon condensate at room temperature. Nat. Commun. 10, 2460 (2019).

    Article  Google Scholar 

  21. Kreil, A. J. E. et al. Tunable space-time crystal in room-temperature magnetodielectrics. Phys. Rev. B 100, 020406 (2019).

    Article  CAS  Google Scholar 

  22. Kreil, A. J. E. et al. From kinetic instability to Bose-Einstein condensation and magnon supercurrents. Phys. Rev. Lett. 121, 077203 (2018).

    Article  CAS  Google Scholar 

  23. Bozhko, D. et al. Supercurrent in a room-temperature Bose–Einstein magnon condensate. Nat. Phys. 12, 1057–1062 (2016).

    Article  CAS  Google Scholar 

  24. Volovik, G. E. On the broken time translation symmetry in macroscopic systems: precessing states and off-diagonal long-range order. JETP Lett. 98, 491–495 (2013).

    Article  CAS  Google Scholar 

  25. Heikkinen, P. J. et al. Relaxation of Bose-Einstein condensates of magnons in magneto-textural traps in superfluid 3He-B. J. Low Temp. Phys. 175, 3–16 (2014).

    Article  CAS  Google Scholar 

  26. Bunkov, Y. M. & Volovik, G. E. Magnon condensation into a Q ball in 3He – B. Phys. Rev. Lett. 98, 265302 (2007).

    Article  Google Scholar 

  27. Autti, S. et al. Self-trapping of magnon Bose-Einstein condensates in the ground state and on excited levels: from harmonic to box confinement. Phys. Rev. Lett. 108, 145303 (2012).

    Article  CAS  Google Scholar 

  28. Thuneberg, E. V. Hydrostatic theory of superfluid 3He-B. J. Low Temp. Phys. 122, 657–682 (2001).

    Article  CAS  Google Scholar 

  29. Autti, S., Heikkinen, P. J., Volovik, G. E., Zavjalov, V. V. & Eltsov, V. B. Propagation of self-localized Q-ball solitons in the 3He universe. Phys. Rev. B 97, 014518 (2018).

    Article  CAS  Google Scholar 

  30. Penrose, R. Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14, 57–59 (1965).

    Article  Google Scholar 

  31. Sato, Y. & Packard, R. E. Superfluid helium quantum interference devices: physics and applications. Rep. Prog. Phys. 75, 016401 (2011).

    Article  Google Scholar 

  32. Kreil, A. J. E. et al. Josephson oscillations in a room-temperature Bose-Einstein magnon condensate. Preprint at arXiv:1911.07802 (2019).

  33. Heikkinen, P. J., Autti, S., Eltsov, V. B., Haley, R. P. & Zavjalov, V. V. Microkelvin thermometry with Bose-Einstein condensates of magnons and applications to studies of the AB interface in superfluid 3He. J. Low Temp. Phys. 175, 681–705 (2014).

    Article  CAS  Google Scholar 

  34. Blaauwgeers, R. et al. Quartz tuning fork: thermometer, pressure- and viscometer for helium liquids. J. Low Temp. Phys. 146, 537–562 (2007).

    Article  CAS  Google Scholar 

  35. Blažková, M. et al. Vibrating quartz fork: a tool for cryogenic helium research. J. Low Temp. Phys. 150, 525–535 (2008).

    Article  Google Scholar 

  36. Heikkinen, P. J. Magnon Bose-Einstein Condensate as a Probe of Topological Superfluid. PhD thesis, Aalto Univ. (2016).

  37. Autti, S. Higgs Bosons, Half-Quantum Vortices, and Q-balls: an Expedition in the 3He Universe. PhD thesis, Aalto Univ. (2017).

  38. Kopu, J. Numerically calculated NMR response from different vortex distributions in superfluid 3He-B. J. Low Temp. Phys. 146, 47–58 (2007).

    Article  CAS  Google Scholar 

  39. Autti, S. et al. AC Josephson effect between two superfluid time crystals. Zenodo https://doi.org/10.5281/zenodo.3878045 (2020).

Download references

Acknowledgements

This work has been supported by the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 694248). The experimental work was carried out in the Low Temperature Laboratory, which is part of the OtaNano research infrastructure of Aalto University and of the European Microkelvin Platform. S.A. acknowledges financial support from the Jenny and Antti Wihuri Foundation, and P.J.H. from the Väisälä Foundation of the Finnish Academy of Science and Letters.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to writing the manuscript and discussing the results. Experiments were carried out and planned and analysis done by S.A., J.T.M, P.J.H, V.V.Z, and V.B.E. Theoretical work was done by S.A., G.E.V, and V.B.E. V.B.E. supervised the project.

Corresponding authors

Correspondence to S. Autti or V. B. Eltsov.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Autti, S., Heikkinen, P.J., Mäkinen, J.T. et al. AC Josephson effect between two superfluid time crystals. Nat. Mater. 20, 171–174 (2021). https://doi.org/10.1038/s41563-020-0780-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-020-0780-y

This article is cited by

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