Abstract
Discrete time quasi-crystals are non-equilibrium phenomena with quasi-periodic order in time domain, an extension of the discrete time-crystal phase. As a natural platform to explore the non-equilibrium phases, Rydberg atomic arrays have demonstrated the quantum simulation of the discrete-time crystal phase, associated with quantum many-body scar state. However, the existence of discrete time quasi-crystal in this platform has yet to be conceived. Here, we propose a method to generate the discrete time quasi-crystal behavior by coupling two discrete time-crystals, where two external driving frequencies have the maximum incommensurability. Upon the characterization of the phase diagram and the robustness, we explore the entanglement entropy between two subsystems. We find that the emergence of the aperiodic response appears at an appropriate driving frequency, which could be well interpreted by the model with two coupled oscillators. Our method thus offers the possibilities to explore the phases of matters in the quantum simulator.
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Data availability
The data generated in this study have been deposited in a Zenodo database under the identifier https://doi.org/10.5281/zenodo.18396451.
Code availability
The code that supports the findings of this study is available from the corresponding author on request.
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Acknowledgements
We thank the helpful discussion with Heng Shen, Zhuangzhuang Tian. This work is supported by the National Key R&D Program of China under Grant No. 2020YFA0309400, NNSFC under Grant Nos. 12222409 and 12174081, 11974228. X.L. acknowledges the Key Research and Development Program of Shanxi Province (Grants No. 202101150101025). W.J. acknowledges the National Natural Science Foundation of China (Project No. 12404275) and the Fundamental Research Program of Shanxi Province (Project No. 202403021212015).
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W.J. conceived the idea. X.L. developed the model and performed all the computational work. Y.Z. and Z.X. contributed to the experimental feasibility. All authors contributed to the paper writing.
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Luo, X., Zhou, Y., Xu, Z. et al. Discrete time quasi-crystals in Rydberg atomic chain. Commun Phys (2026). https://doi.org/10.1038/s42005-026-02572-0
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DOI: https://doi.org/10.1038/s42005-026-02572-0
