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Observation of chiral state transfer without encircling an exceptional point

Nature volume 605, pages 256–261 (2022)Cite this article

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Abstract

The adiabatic theorem, a corollary of the Schrödinger equation, manifests itself in a profoundly different way in non-Hermitian arrangements, resulting in counterintuitive state transfer schemes that have no counterpart in closed quantum systems. In particular, the dynamical encirclement of exceptional points (EPs) in parameter space has been shown to lead to a chiral phase accumulation, non-adiabatic jumps and topological mode conversion1,2,3,4,5,6,7,8. Recent theoretical studies, however, have shown that contrary to previously established demonstrations, this behaviour is not strictly a result of winding around a non-Hermitian degeneracy9. Instead, it seems to be mostly attributed to the non-trivial landscape of the Riemann surfaces, sometimes because of the presence of an EP in the vicinity9,10,11. Here, in an effort to bring this counterintuitive aspect of non-Hermitian systems to light and confirm this hypothesis, we provide a set of experiments to directly observe the field evolution and chiral state conversion in an EP-excluding cycle in a slowly varying non-Hermitian system. To do so, a versatile yet unique fibre-based photonic emulator is realized that utilizes the polarization degrees of freedom in a quasi-common-path single-ring arrangement. Our observations may open up new avenues for light manipulation and state conversion, as well as providing a foundation for understanding the intricacies of the adiabatic theorem in non-Hermitian systems.

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Fig. 1: Self-intersecting Riemann manifolds in the gain-phase parameter space and chiral mode conversion.
Fig. 2: Operation principle of the devised fibre-based photonic emulator.
Fig. 3: Polarization stability and coupling between the polarization components of a light pulse.
Fig. 4: Experimental observation of chiral mode conversion through a parametric steering of the Hamiltonian along a trajectory that lies in the proximity of an EP.

Data availability

All data that support the findings of this study are available within the paper and the Supplementary Information and are available from the corresponding author upon request.

References

  1. Uzdin, R., Mailybaev, A. & Moiseyev, N. On the observability and asymmetry of adiabatic state flips generated by exceptional points. J. Phys. A 44, 435302 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  2. Graefe, E.-M., Mailybaev, A. A. & Moiseyev, N. Breakdown of adiabatic transfer of light in waveguides in the presence of absorption. Phys. Rev. A 88, 033842 (2013).

    Article  ADS  Google Scholar 

  3. Gilary, I., Mailybaev, A. A. & Moiseyev, N. Time-asymmetric quantum-state-exchange mechanism. Phys. Rev. A 88, 010102 (2013).

    Article  ADS  Google Scholar 

  4. Doppler, J. et al. Dynamically encircling an exceptional point for asymmetric mode switching. Nature 537, 76–79 (2016).

    Article  ADS  CAS  Google Scholar 

  5. Xu, H., Mason, D., Jiang, L. & Harris, J. G. Topological energy transfer in an optomechanical system with exceptional points. Nature 537, 80–83 (2016).

    Article  ADS  CAS  Google Scholar 

  6. Yoon, J. W. et al. Time-asymmetric loop around an exceptional point over the full optical communications band. Nature 562, 86–90 (2018).

    Article  ADS  CAS  Google Scholar 

  7. Hassan, A. U., Zhen, B., Soljačić, M., Khajavikhan, M. & Christodoulides, D. N. Dynamically encircling exceptional points: exact evolution and polarization state conversion. Phys. Rev. Lett. 118, 093002 (2017).

    Article  ADS  Google Scholar 

  8. Zhang, X.-L. & Chan, C. T. Dynamically encircling exceptional points in a three-mode waveguide system. Commun. Phys. 2, 63 (2019).

    Article  Google Scholar 

  9. Hassan, A. U. et al. Chiral state conversion without encircling an exceptional point. Phys. Rev. A 96, 052129 (2017).

    Article  ADS  Google Scholar 

  10. Zhong, Q., Khajavikhan, M., Christodoulides, D. N. & El-Ganainy, R. Winding around non-Hermitian singularities. Nat. Commun. 9, 4808 (2018).

    Article  ADS  Google Scholar 

  11. Feilhauer, J. et al. Encircling exceptional points as a non-Hermitian extension of rapid adiabatic passage. Phys. Rev. A 102, 040201 (2020).

    Article  ADS  CAS  Google Scholar 

  12. Kato, T. Perturbation Theory for Linear Operators (Springer, 2013).

  13. Heiss, W. D. Phases of wave functions and level repulsion. Eur. Phys. J. D 7, 1–4 (1999).

    Article  ADS  CAS  Google Scholar 

  14. Moiseyev, N. Non-Hermitian Quantum Mechanics (Cambridge Univ. Press, 2011).

  15. El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).

    Article  CAS  Google Scholar 

  16. Parto, M., Liu, Y. G. N., Bahari, B., Khajavikhan, M. & Christodoulides, D. N. Non-Hermitian and topological photonics: optics at an exceptional point. Nanophotonics 10, 403–423 (2021).

    Article  Google Scholar 

  17. Makris, K. G., El-Ganainy, R., Christodoulides, D. N. & Musslimani, Z. H. Beam dynamics in PT symmetric optical lattices. Phys. Rev. Lett. 100, 103904 (2008).

    Article  ADS  CAS  Google Scholar 

  18. Klaiman, S., Günther, U. & Moiseyev, N. Visualization of branch points in PT-symmetric waveguides. Phys. Rev. Lett. 101, 080402 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  19. Zheng, M. C., Christodoulides, D. N., Fleischmann, R. & Kottos, T. PT optical lattices and universality in beam dynamics. Phys. Rev. A 82, 010103 (2010).

    Article  ADS  Google Scholar 

  20. Milburn, T. J. et al. General description of quasiadiabatic dynamical phenomena near exceptional points. Phys. Rev. A 92, 052124 (2015).

    Article  ADS  Google Scholar 

  21. Zhang, X.-L., Wang, S., Hou, B. & Chan, C. T. Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point. Phys. Rev. X 8, 021066 (2018).

    CAS  Google Scholar 

  22. Zhang, X.-L., Jiang, T. & Chan, C. T. Dynamically encircling an exceptional point in anti-parity-time symmetric systems: asymmetric mode switching for symmetry-broken modes. Light Sci. Appl. 8, 88 (2019).

    Article  ADS  Google Scholar 

  23. Choi, Y., Hahn, C., Yoon, J. W., Song, S. H. & Berini, P. Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points. Nat. Commun. 8, 14154 (2017).

    Article  ADS  CAS  Google Scholar 

  24. Choi, Y., Yoon, J. W., Hong, J. K., Ryu, Y. & Song, S. H. Direct observation of time-asymmetric breakdown of the standard adiabaticity around an exceptional point. Commun. Phys. 3, 140 (2020).

    Article  Google Scholar 

  25. Gao, T. et al. Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard. Nature 526, 554–558 (2015).

    Article  ADS  CAS  Google Scholar 

  26. Dembowski, C. et al. Experimental observation of the topological structure of exceptional points. Phys. Rev. Lett. 86, 787 (2001).

    Article  ADS  CAS  Google Scholar 

  27. Mailybaev, A. A., Kirillov, O. N. & Seyranian, A. P. Geometric phase around exceptional points. Phys. Rev. A 72, 014104 (2005).

    Article  ADS  Google Scholar 

  28. Heiss, W. D. The physics of exceptional points. J. Phys. A 45, 444016 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  29. Dembowski, C. et al. Encircling an exceptional point. Phys. Rev. E 69, 056216 (2004).

    Article  ADS  CAS  Google Scholar 

  30. Liu, Q., Liu, J., Zhao, D. & Wang, B. On-chip experiment for chiral mode transfer without enclosing an exceptional point. Phys. Rev. A 103, 023531 (2021).

    Article  ADS  CAS  Google Scholar 

  31. Berry, M. V. & Uzdin, R. Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon. J. Phys. A 44, 435303 (2011).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge the financial support from the Air Force Office of Scientific Research (Multidisciplinary University Research Initiative (MURI) Award on Novel light-matter interactions in topologically non-trivial Weyl semimetal structures and systems: FA9550-20-1-0322,  MURI Award on Programmable systems with non-Hermitian quantum dynamics: FA9550-21-1-0202), DARPA (D18AP00058), the Office of Naval Research (N00014-19-1-2052, N00014-20-1-2522, MURI Award on Classical entanglement in structured optical fields: N00014-20-1-2789), the Army Research Office (W911NF-17-1-0481), the National Science Foundation (DMR-1420620, EECS-1711230, ECCS CBET 1805200, ECCS 2000538, ECCS 2011171), the W. M. Keck Foundation, the US–Israel Binational Science Foundation (BSF; 2016381), the MPS Simons collaboration (Simons grant 733682), the US Air Force Research Laboratory (FA86511820019), the Austrian Science Fund (FWF, P32300 WAVELAND) and European Commission grant MSCA-RISE 691209. G.L-G. acknowledges support from Consejo Nacional de Ciencia y Tecnologia (CONACyT). We thank A. Turchanin and U. Peschel from Friedrich Schiller University Jena for useful discussions and feedback.

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Authors and Affiliations

  1. Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA

    Hadiseh Nasari, Alexander Schumer & Mercedeh Khajavikhan

  2. CREOL, The College of Optics & Photonics, University of Central Florida, Orlando, FL, USA

    Hadiseh Nasari, Gisela Lopez-Galmiche, Helena E. Lopez-Aviles, Absar U. Hassan, Qi Zhong, Patrick LiKamWa & Demetrios N. Christodoulides

  3. Institute for Theoretical Physics, Vienna University of Technology (TU Wien), Vienna, Austria

    Alexander Schumer & Stefan Rotter

  4. Department of Physics & Astronomy, University of Southern California, Los Angeles, CA, USA

    Mercedeh Khajavikhan

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  1. Hadiseh Nasari
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Contributions

D.N.C. and M.K. conceived the idea. H.N., G.L.-G. and H.E.L.-A. designed and performed the experiments in consultation with other team members. H.N., A.U.H. and A.S. performed the analysis with help from other members. H.N., M.K. and D.N.C. wrote the manuscript with help from all the authors.

Corresponding author

Correspondence to Mercedeh Khajavikhan.

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Nature thanks Jae Woong Yoon and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Nasari, H., Lopez-Galmiche, G., Lopez-Aviles, H.E. et al. Observation of chiral state transfer without encircling an exceptional point. Nature 605, 256–261 (2022). https://doi.org/10.1038/s41586-022-04542-2

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