Non-Hermitian Exceptional Topology on a Klein Bottle Photonic Circuit

TL;DR

This paper demonstrates a scalable silicon photonic circuit that emulates non-Hermitian Hamiltonians on a Klein bottle topology, revealing novel exceptional topological phases and nontrivial Fermi arc structures.

Contribution

It introduces a reconfigurable photonic platform for simulating non-Hermitian topological models on nonorientable manifolds, enabling experimental exploration of exotic exceptional phases.

Findings

First photonic realization of exceptional topology on a Klein bottle

Mapping of Fermi arc revealing nontrivial exceptional topology

Identification of same-charge EPs (EP monopoles) that cannot annihilate locally

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.