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# 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.

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## 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.

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## 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

### 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.

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Reprints and Permissions

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

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