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Interferometric Readout of Momentum-Space Topology in a Programmable Dissipative Photonic Circuit

Andrea Cataldo1,*, Emil J. Bergholtz2, Daniel Leykam3, Jun Gao4,5,6,†, and Ali W. Elshaari1,‡

  • *Contact author: andreacl@kth.se
  • †Contact author: jungao@hust.edu.cn
  • ‡Contact author: elshaari@kth.se
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Phys. Rev. Lett. 137, 206601 – Published 12 November, 2026

DOI: https://doi.org/10.1103/xkht-64kc

Abstract

Topology under non-Hermitian dynamics is encoded in the phase of the bulk evolution, yet strong dissipation suppresses the amplitudes carrying it. We resolve this using a programmable photonic integrated circuit that implements such dynamics in synthetic momentum space through unitary dilation, with the phase recovered by phase-shifted interferometry. For the non-Hermitian Su-Schrieffer-Heeger model, the method distinguishes trivial and nontrivial Zak phases and yields a coherence winding q=±1 induced by an exceptional point. Extending to a synthetic torus via a Rice-Mele pump gives the first Chern number Ch1=0, 1 for trivial and nontrivial cycles, showing a programmable route to momentum-space topology under strongly dissipative non-Hermitian dynamics.

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References (34)

  1. M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, Imaging topological edge states in silicon photonics, Nat. Photonics 7, 1001 (2013).
  2. Jiho Noh, Sheng Huang, Kevin P. Chen, and Mikael C. Rechtsman, Observation of photonic topological valley Hall edge states, Phys. Rev. Lett. 120, 063902 (2018).
  3. Tomoki Ozawa, Hannah M. Price, Alberto Amo, Nathan Goldman, Mohammad Hafezi, Ling Lu, Mikael C. Rechtsman, David Schuster, Jonathan Simon, Oded Zilberberg, and Iacopo Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
  4. Filippo Cardano, Alessio D’Errico, Alexandre Dauphin, Maria Maffei, Bruno Piccirillo, Corrado De Lisio, Giulio De Filippis, Vittorio Cataudella, Enrico Santamato, Lorenzo Marrucci, Maciej Lewenstein, and Pietro Massignan, Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons, Nat. Commun. 8, 15516 (2017).
  5. S. Longhi, Probing one-dimensional topological phases in waveguide lattices with broken chiral symmetry, Opt. Lett. 43, 4639 (2018).
  6. Stefano Longhi, Probing topological phases in waveguide superlattices, Opt. Lett. 44, 2530 (2019).
  7. Yao Wang, Yong-Heng Lu, Feng Mei, Jun Gao, Zhan-Ming Li, Hao Tang, Shi-Liang Zhu, Suotang Jia, and Xian-Min Jin, Direct observation of topology from single-photon dynamics, Phys. Rev. Lett. 122, 193903 (2019).
  8. Zhi-Qiang Jiao, Stefano Longhi, Xiao-Wei Wang, Jun Gao, Wen-Hao Zhou, Yao Wang, Yu-Xuan Fu, Li Wang, Ruo-Jing Ren, Lu-Feng Qiao, and Xian-Min Jin, Experimentally detecting quantized Zak phases without chiral symmetry in photonic lattices, Phys. Rev. Lett. 127, 147401 (2021).
  9. Ze-Sheng Xu, Jun Gao, Govind Krishna, Stephan Steinhauer, Val Zwiller, and Ali W. Elshaari, Direct measurement of topological invariants in photonic superlattices, Photonics Res. 10, 2901 (2022).
  10. Julia M. Zeuner, Mikael C. Rechtsman, Yonatan Plotnik, Yaakov Lumer, Stefan Nolte, Mark S. Rudner, Mordechai Segev, and Alexander Szameit, Observation of a topological transition in the bulk of a non-Hermitian system, Phys. Rev. Lett. 115, 040402 (2015).
  11. Shunyu Yao and Zhong Wang, Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett. 121, 086803 (2018).
  12. Flore K. Kunst, Elisabet Edvardsson, Jan Carl Budich, and Emil J. Bergholtz, Biorthogonal bulk-boundary correspondence in non-Hermitian systems, Phys. Rev. Lett. 121, 026808 (2018).
  13. Daniel Leykam and Daria A. Smirnova, Probing bulk topological invariants using leaky photonic lattices, Nat. Phys. 17, 632 (2021).
  14. Maria Maffei, Alexandre Dauphin, Filippo Cardano, Maciej Lewenstein, and Pietro Massignan, Topological characterization of chiral models through their long time dynamics, New J. Phys. 20, 013023 (2018).
  15. Wen Sheng Gao, Meng Xiao, C. T. Chan, and Wing Yim Tam, Determination of Zak phase by reflection phase in 1D photonic crystals, Opt. Lett. 40, 5259 (2015).
  16. Maxim A. Gorlach, Xiang Ni, Daria A. Smirnova, Dmitry Korobkin, Dmitry Zhirihin, Alexey P. Slobozhanyuk, Pavel A. Belov, Andrea Alù, and Alexander B. Khanikaev, Far-field probing of leaky topological states in all-dielectric metasurfaces, Nat. Commun. 9, 909 (2018).
  17. C. Liu, H. R. Wang, and H. C. Ong, Determination of the Zak phase of one-dimensional diffractive systems with inversion symmetry via radiation in Fourier space, Phys. Rev. B 108, 035403 (2023).
  18. Ki Young Lee, Kwang Wook Yoo, Youngsun Choi, Gunpyo Kim, Sangmo Cheon, Jae Woong Yoon, and Seok Ho Song, Topological guided-mode resonances at non-Hermitian nanophotonic interfaces, Nanophotonics 10, 1853 (2021).
  19. Ramy El-Ganainy, Konstantinos G. Makris, Mercedeh Khajavikhan, Ziad H. Musslimani, Stefan Rotter, and Demetrios N. Christodoulides, Non-Hermitian physics and PT symmetry, Nat. Phys. 14, 11 (2018).
  20. Emil J. Bergholtz, Jan Carl Budich, and Flore K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
  21. Wim Bogaerts, Daniel Pérez, José Capmany, David A. B. Miller, Joyce Poon, Dirk Englund, Francesco Morichetti, and Andrea Melloni, Programmable photonic circuits, Nature (London) 586, 207 (2020).
  22. Mehmet Berkay On, Farshid Ashtiani, David Sanchez-Jacome, Daniel Perez-Lopez, S. J. Ben Yoo, and Andrea Blanco-Redondo, Programmable integrated photonics for topological Hamiltonians, Nat. Commun. 15, 629 (2024).
  23. Shirong Lin, Luojia Wang, Luqi Yuan, and Xianfeng Chen, All-optical control of the photonic Hall lattice in a pumped waveguide array, Phys. Rev. Appl. 17, 064029 (2022).
  24. Ze-Sheng Xu, J. Lukas K. König, Andrea Cataldo, Rohan Yadgirkar, Govind Krishna, Venkatesh Deenadayalan, Val Zwiller, Stefan Preble, Emil J. Bergholtz, Jun Gao, and Ali W. Elshaari, Non-Hermitian exceptional topology on a Klein bottle photonic circuit, Light: Sci. Appl. 15, 390 (2026).
  25. Zixuan Hu, Rongxin Xia, and Sabre Kais, A quantum algorithm for evolving open quantum dynamics on quantum computing devices, Sci. Rep. 10, 3301 (2020).
  26. Yang Wu, Wenquan Liu, Jianpei Geng, Xingrui Song, Xiangyu Ye, Chang-Kui Duan, Xing Rong, and Jiangfeng Du, Observation of parity-time symmetry breaking in a single-spin system, Science 364, 878 (2019).
  27. Shruti Dogra, Artem A. Melnikov, and Gheorghe Sorin Paraoanu, Quantum simulation of parity–time symmetry breaking with a superconducting quantum processor, Commun. Phys. 4, 26 (2021).
  28. See Supplemental Material at http://link.aps.org/supplemental/10.1103/xkht-64kc for supporting theory and methodological details, which includes Ref. [29].
  29. William R. Clements, Peter C. Humphreys, Benjamin J. Metcalf, W. Steven Kolthammer, and Ian A. Walmsley, Optimal design for universal multiport interferometers, Optica 3, 1460 (2016).
  30. P. Hariharan, Optical Interferometry, 2nd ed. (Elsevier Academic Press, Amsterdam, 2003).
  31. Andreas Fyrillas, Olivier Faure, Nicolas Maring, Jean Senellart, and Nadia Belabas, Scalable machine learning-assisted clear-box characterization for optimally controlled photonic circuits, Optica 11, 427 (2024).
  32. Jin-Hao Zheng, Qin-Qin Wang, Lan-Tian Feng, Yu-Yang Ding, Xiao-Ye Xu, Xi-Feng Ren, Chuan-Feng Li, and Guang-Can Guo, Global calibration of large-scale photonic integrated circuits, Phys. Rev. Appl. 22, 054011 (2024).
  33. ZeYang Fan, JunMin Lin, Tian Zhang, Jian Dai, XingYuan Xu, and Kun Xu, Efficient off-chip configuration method for scalable programmable photonic integrated circuits, Commun. Phys. 8, 218 (2025).
  34. D. J. Thouless, Quantization of particle transport, Phys. Rev. B 27, 6083 (1983).

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Phys. Rev. Lett. 137, 206601– Published 12 November, 2026
  • Received 24 May 2026
  • Revised 24 September 2026
  • Accepted 28 September 2026
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