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Topological complex-energy braiding of non-Hermitian bands

Author

Listed:
  • Kai Wang

    (Stanford University)

  • Avik Dutt

    (Stanford University)

  • Charles C. Wojcik

    (Stanford University)

  • Shanhui Fan

    (Stanford University)

Abstract

Effects connected with the mathematical theory of knots1 emerge in many areas of science, from physics2,3 to biology4. Recent theoretical work discovered that the braid group characterizes the topology of non-Hermitian periodic systems5, where the complex band energies can braid in momentum space. However, such braids of complex-energy bands have not been realized or controlled experimentally. Here, we introduce a tight-binding lattice model that can achieve arbitrary elements in the braid group of two strands š¯”¹2. We experimentally demonstrate such topological complex-energy braiding of non-Hermitian bands in a synthetic dimension6,7. Our experiments utilize frequency modes in two coupled ring resonators, one of which undergoes simultaneous phase and amplitude modulation. We observe a wide variety of two-band braiding structures that constitute representative instances of links and knots, including the unlink, the unknot, the Hopf link and the trefoil. We also show that the handedness of braids can be changed. Our results provide a direct demonstration of the braid-group characterization of non-Hermitian topology and open a pathway for designing and realizing topologically robust phases in open classical and quantum systems.

Suggested Citation

  • Kai Wang & Avik Dutt & Charles C. Wojcik & Shanhui Fan, 2021. "Topological complex-energy braiding of non-Hermitian bands," Nature, Nature, vol. 598(7879), pages 59-64, October.
  • Handle: RePEc:nat:nature:v:598:y:2021:i:7879:d:10.1038_s41586-021-03848-x
    DOI: 10.1038/s41586-021-03848-x
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    Citations

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    Cited by:

    1. Yaowen Hu & Mengjie Yu & Neil Sinclair & Di Zhu & Rebecca Cheng & Cheng Wang & Marko LonĨar, 2022. "Mirror-induced reflection in the frequency domain," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    2. Chitres Guria & Qi Zhong & Sahin Kaya Ozdemir & Yogesh S. S. Patil & Ramy El-Ganainy & Jack Gwynne Emmet Harris, 2024. "Resolving the topology of encircling multiple exceptional points," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
    3. Qiuyan Zhou & Jien Wu & Zhenhang Pu & Jiuyang Lu & Xueqin Huang & Weiyin Deng & Manzhu Ke & Zhengyou Liu, 2023. "Observation of geometry-dependent skin effect in non-Hermitian phononic crystals with exceptional points," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    4. Midya Parto & Christian Leefmans & James Williams & Franco Nori & Alireza Marandi, 2023. "Non-Abelian effects in dissipative photonic topological lattices," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    5. Jamal H. Busnaina & Zheng Shi & Alexander McDonald & Dmytro Dubyna & Ibrahim Nsanzineza & Jimmy S. C. Hung & C. W. Sandbo Chang & Aashish A. Clerk & Christopher M. Wilson, 2024. "Quantum simulation of the bosonic Kitaev chain," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    6. Zhen Li & Li-Wei Wang & Xulong Wang & Zhi-Kang Lin & Guancong Ma & Jian-Hua Jiang, 2024. "Observation of dynamic non-Hermitian skin effects," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    7. Shulin Wang & Chengzhi Qin & Weiwei Liu & Bing Wang & Feng Zhou & Han Ye & Lange Zhao & Jianji Dong & Xinliang Zhang & Stefano Longhi & Peixiang Lu, 2022. "High-order dynamic localization and tunable temporal cloaking in ac-electric-field driven synthetic lattices," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    8. Avik Dutt & Luqi Yuan & Ki Youl Yang & Kai Wang & Siddharth Buddhiraju & Jelena VuĨković & Shanhui Fan, 2022. "Creating boundaries along a synthetic frequency dimension," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    9. Xuewei Zhang & Chaohua Wu & Mou Yan & Ni Liu & Ziyu Wang & Gang Chen, 2024. "Observation of continuum Landau modes in non-Hermitian electric circuits," Nature Communications, Nature, vol. 15(1), pages 1-7, December.

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