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Multiblock exceptional points in open quantum systems

Aysel Shiralieva, Grigory A. Starkov, and Björn Trauzettel

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Phys. Rev. A 113, 052202 – Published 4 May, 2026

DOI: https://doi.org/10.1103/gtw6-yn95

Abstract

Open quantum systems can be approximately described by non-Hermitian Hamiltonians (NHHs) and Liouvillian superoperators. The two approaches differ by quantum jump terms corresponding to a measurement of the system by its environment. We analyze the emergence of exceptional points (EPs) in NHHs and Liouvillian superoperators. In particular, we show how EPs in NHHs relate to a different type of EPs—multiblock EPs—in the no-jump Liouvillian, i.e., the Liouvillian superoperator in absence of quantum jump terms. We further analyze how quantum jump terms modify the multiblock structure. To illustrate our general findings, we present two prime examples: qubits and qutrits coupled to additional ground-state levels that serve as sinks of the population. In those examples, we can navigate through the EP block structure by a variation of physical parameters. We analyze how the dynamics of the population of the states is affected by the order of the EPs. Additionally, we demonstrate that the quantum geometric tensor serves as a sensitive indicator of EPs of different kinds.

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References (40)

  1. Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
  2. H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, Enhanced sensitivity at higher-order exceptional points, Nature (London) 548, 187 (2017).
  3. J. Wiersig, Review of exceptional point-based sensors, Photon. Res. 8, 1457 (2020).
  4. J. Feilhauer, A. Schumer, J. Doppler, A. A. Mailybaev, J. Böhm, U. Kuhl, N. Moiseyev, and S. Rotter, Encircling exceptional points as a non-Hermitian extension of rapid adiabatic passage, Phys. Rev. A 102, 040201(R) (2020).
  5. Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Topological phases of non-Hermitian systems, Phys. Rev. X 8, 031079 (2018).
  6. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
  7. N. Okuma and M. Sato, Non-Hermitian topological phenomena: A review, Annu. Rev. Condens. Matter Phys. 14, 83 (2023).
  8. C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus, Selective enhancement of topologically induced interface states in a dielectric resonator chain, Nat. Commun. 6, 6710 (2015).
  9. J. M. Zeuner, M. C. Rechtsman, Y. Plotnik, Y. Lumer, S. Nolte, M. S. Rudner, M. Segev, and A. Szameit, Observation of a topological transition in the bulk of a non-Hermitian system, Phys. Rev. Lett. 115, 040402 (2015).
  10. S. Weimann, M. Kremer, Y. Plotnik, Y. Lumer, S. Nolte, K. G. Makris, M. Segev, M. C. Rechtsman, and A. Szameit, Topologically protected bound states in photonic parity–time-symmetric crystals, Nat. Mater. 16, 433 (2017).
  11. A. Cerjan, S. Huang, M. Wang, K. P. Chen, Y. Chong, and M. C. Rechtsman, Experimental realization of a Weyl exceptional ring, Nat. Photonics 13, 623 (2019).
  12. W. Chen, c. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, Exceptional points enhance sensing in an optical microcavity, Nature (London) 548, 192 (2017).
  13. M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science 359, eaar4005 (2018).
  14. A. Dikopoltsev, T. H. Harder, E. Lustig, O. A. Egorov, J. Beierlein, A. Wolf, Y. Lumer, M. Emmerling, C. Schneider, S. Höfling, M. Segev, and S. Klembt, Topological insulator vertical-cavity laser array, Science 373, 1514 (2021).
  15. H. Zhou, C. Peng, Y. Yoon, C. W. Hsu, K. A. Nelson, L. Fu, J. D. Joannopoulos, M. Soljačić, and B. Zhen, Observation of bulk Fermi arc and polarization half charge from paired exceptional points, Science 359, 1009 (2018).
  16. T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L. W. Molenkamp, C. H. Lee, A. Szameit, M. Greiter, and R. Thomale, Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits, Nat. Phys. 16, 747 (2020).
  17. A. Kodigala, T. Lepetit, and B. Kanté, Exceptional points in three-dimensional plasmonic nanostructures, Phys. Rev. B 94, 201103(R) (2016).
  18. C. Wang, Z. Fu, W. Mao, J. Qie, A. D. Stone, and L. Yang, Non-Hermitian optics and photonics: from classical to quantum, Adv. Opt. Photon. 15, 442 (2023).
  19. F. Minganti, A. Miranowicz, R. W. Chhajlany, and F. Nori, Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps, Phys. Rev. A 100, 062131 (2019).
  20. W. Chen, M. Abbasi, B. Ha, S. Erdamar, Y. N. Joglekar, and K. W. Murch, Decoherence-induced exceptional points in a dissipative superconducting qubit, Phys. Rev. Lett. 128, 110402 (2022).
  21. J. Wiersig, Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies, Phys. Rev. A 101, 053846 (2020).
  22. S. Bid and H. Schomerus, Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point, Phys. Rev. Res. 7, 023062 (2025).
  23. S. Bid and H. Schomerus, Fragmented exceptional points and their bulk and edge realizations in lattice models Phys. Rev. B 112, 195433 (2025).
  24. F. Minganti, A. Miranowicz, R. W. Chhajlany, I. I. Arkhipov, and F. Nori, Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories, Phys. Rev. A 101, 062112 (2020).
  25. L. Sá, P. Ribeiro, and T. Prosen, Symmetry classification of many-body Lindbladians: Tenfold way and beyond, Phys. Rev. X 13, 031019 (2023).
  26. M. Naghiloo, Y. N. Joglekar, and K. W. Murch, Quantum state tomography across the exceptional point in a single dissipative qubit, Nat. Phys. 15, 1232 (2019).
  27. W. Chen, M. Abbasi1, Y. N. Joglekar, and K. W. Murch, Quantum jumps in the non-Hermitian dynamics of a superconducting qubit, Phys. Rev. Lett. 127, 140504 (2021).
  28. V. Lidskii, Perturbation theory of non-conjugate operators, USSR Comput. Math. Math. Phys. 6, 73 (1966).
  29. J. Moro, J. V. Burke, and M. L. Overton, On the Lidskii–Vishik–Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure, SIAM J. Matrix Anal. Appl. 18, 793 (1997).
  30. J. Moro and F. M. Dopico, First order eigenvalue perturbation theory and the Newton diagram, in Applied Mathematics and Scientific Computing, edited by Z. Drmač, V. Hari, L. Sopta, Z. Tutek, and K. Veselić (Springer, Boston, 2003), pp. 143–175.
  31. S. Sayyad and G. A. Starkov, Characterizing all non-Hermitian degeneracies using algebraic approaches: Defectiveness and asymptotic behavior, arXiv:2604.16140.
  32. J. P. Provost and G. Vallee, Riemannian structure on manifolds of quantum states, Commun. Math. Phys. 76, 289 (1980).
  33. D. D. Solnyshkov, C. Leblanc, L. Bessonart, A. Nalitov, J. Ren, Q. Liao, F. Li, and G. Malpuech, Quantum metric and wave packets at exceptional points in non-Hermitian systems, Phys. Rev. B 103, 125302 (2021).
  34. P. Orlov, G. V. Shlyapnikov, and D. V. Kurlov, Adiabatic transformations in dissipative and non-Hermitian phase transitions, Phys. Rev. B 111, L081105 (2025).
  35. Q. Liao, C. Leblanc, J. Ren, F. Li, Y. Li, D. Solnyshkov, G. Malpuech, J. Yao, and H. Fu, Experimental measurement of the divergent quantum metric of an exceptional point, Phys. Rev. Lett. 127, 107402 (2021).
  36. D. Brody and E.-M. Graefe, Information geometry of complex Hamiltonians and exceptional points, Entropy 15, 3361 (2013).
  37. Y.-M. R. Hu, E. A. Ostrovskaya, and E. Estrecho, Generalized quantum geometric tensor in a non-Hermitian exciton-polariton system, Opt. Mater. Express 14, 664 (2024).
  38. G. A. Starkov, M. V. Fistul, and I. M. Eremin, Formation of exceptional points in pseudo-Hermitian systems, Phys. Rev. A 108, 022206 (2023).
  39. A “reverse engineering” approach reveals that this perturbation requires terms proportional to (|i〉〈h|)⊗(|e〉〈h|)+(|e〉〈h|)⊗(|i〉〈h|).
  40. A. Trampus, A canonical basis for the matrix transformation X→AX+XB, J. Math. Anal. Appl. 14, 242 (1966).

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Phys. Rev. A 113, 052202– Published 4 May, 2026
  • Received 23 September 2025
  • Revised 29 January 2026
  • Accepted 16 March 2026
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