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Winding around non-Hermitian singularities

Author

Listed:
  • Qi Zhong

    (Michigan Technological University)

  • Mercedeh Khajavikhan

    (University of Central Florida)

  • Demetrios N. Christodoulides

    (University of Central Florida)

  • Ramy El-Ganainy

    (Michigan Technological University
    Max Planck Institute for the Physics of Complex Systems)

Abstract

Non-Hermitian singularities are ubiquitous in non-conservative open systems. Owing to their peculiar topology, they can remotely induce observable effects when encircled by closed trajectories in the parameter space. To date, a general formalism for describing this process beyond simple cases is still lacking. Here we develop a general approach for treating this problem by utilizing the power of permutation operators and representation theory. This in turn allows us to reveal a surprising result that has so far escaped attention: loops that enclose the same singularities in the parameter space starting from the same point and traveling in the same direction, do not necessarily share the same end outcome. Interestingly, we find that this equivalence can be formally established only by invoking the topological notion of homotopy. Our findings are general with far reaching implications in various fields ranging from photonics and atomic physics to microwaves and acoustics.

Suggested Citation

  • Qi Zhong & Mercedeh Khajavikhan & Demetrios N. Christodoulides & Ramy El-Ganainy, 2018. "Winding around non-Hermitian singularities," Nature Communications, Nature, vol. 9(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:9:y:2018:i:1:d:10.1038_s41467-018-07105-0
    DOI: 10.1038/s41467-018-07105-0
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    Cited by:

    1. 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.
    2. A. Hashemi & K. Busch & D. N. Christodoulides & S. K. Ozdemir & R. El-Ganainy, 2022. "Linear response theory of open systems with exceptional points," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    3. Ievgen I. Arkhipov & Adam Miranowicz & Fabrizio Minganti & Şahin K. Özdemir & Franco Nori, 2023. "Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch," Nature Communications, Nature, vol. 14(1), pages 1-9, December.

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