Non-Hermitian exceptional topology on a Klein bottle photonic circuit
Abstract
Non-Hermitian physics has unlocked a wealth of unconventional wave phenomena beyond the reach of Hermitian systems, with exceptional points (EPs) driving enhanced sensitivity, nonreciprocal transport, and topological behavior unique to non-Hermitian degeneracies. Here, we present a scalable and reconfigurable silicon photonic integrated circuit capable of emulating arbitrary non-Hermitian time evolution with high precision. Using this programmable platform, we implement a two-band non-Hermitian Hamiltonian defined on a Klein-bottle topology, a nonorientable parameter space that enables exceptional phases forbidden on orientable manifolds. Through an on-chip amplitude-and-phase reconstruction protocol, we retrieve the full complex Hamiltonian at multiple points in parameter space and experimentally map the associated Fermi arc where the imaginary eigenvalue gap closes. The orientation of the measured Fermi arc reveals a nontrivial exceptional topology: it implies the presence of same-charge EPs (or an EP monopole) that cannot annihilate locally on the Klein bottle. Our results demonstrate the first photonic realization of exceptional topology on a nonorientable manifold and establish a versatile platform for exploring exotic non-Hermitian and topological models relevant to classical and quantum photonics.
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BibTeX
@article{xu2026nonhermitian,
title = {{Non-Hermitian exceptional topology on a Klein bottle photonic circuit}},
author = {Ze-Sheng Xu and J. Lukas K. König and Andrea Cataldo and Rohan Yadgirkar and Govind Krishna and Venkatesh Deenadayalan and Val Zwiller and Stefan Preble and Emil J. Bergholtz and Jun Gao and Ali W. Elshaari},
journal = {Light: Science \& Applications},
year = {2026},
month = oct,
doi = {10.1038/s41377-026-02516-x},
url = {https://www.nature.com/articles/s41377-026-02516-x},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Non-Hermitian exceptional topology on a Klein bottle photonic circuit
AU - Ze-Sheng Xu
AU - J. Lukas K. König
AU - Andrea Cataldo
AU - Rohan Yadgirkar
AU - Govind Krishna
AU - Venkatesh Deenadayalan
AU - Val Zwiller
AU - Stefan Preble
AU - Emil J. Bergholtz
AU - Jun Gao
AU - Ali W. Elshaari
PY - 2026
DA - 2026/10/21
JO - Light: Science & Applications
DO - 10.1038/s41377-026-02516-x
UR - https://www.nature.com/articles/s41377-026-02516-x
AB - Non-Hermitian physics has unlocked a wealth of unconventional wave phenomena beyond the reach of Hermitian systems, with exceptional points (EPs) driving enhanced sensitivity, nonreciprocal transport, and topological behavior unique to non-Hermitian degeneracies. Here, we present a scalable and reconfigurable silicon photonic integrated circuit capable of emulating arbitrary non-Hermitian time evolution with high precision. Using this programmable platform, we implement a two-band non-Hermitian Hamiltonian defined on a Klein-bottle topology, a nonorientable parameter space that enables exceptional phases forbidden on orientable manifolds. Through an on-chip amplitude-and-phase reconstruction protocol, we retrieve the full complex Hamiltonian at multiple points in parameter space and experimentally map the associated Fermi arc where the imaginary eigenvalue gap closes. The orientation of the measured Fermi arc reveals a nontrivial exceptional topology: it implies the presence of same-charge EPs (or an EP monopole) that cannot annihilate locally on the Klein bottle. Our results demonstrate the first photonic realization of exceptional topology on a nonorientable manifold and establish a versatile platform for exploring exotic non-Hermitian and topological models relevant to classical and quantum photonics.
SN - 2047-7538
SN - 2095-5545
ER -