Exceptional Topological Signatures of Non-Hermitian Photonic Hopf-Link Braids
Abstract
Non-Hermitian physics endows the non-Abelian systems with exceptional topology characterized by non-commutative braid patterns. Interplay of distinct competing sources of non-Hermiticity may induce novel topological effects. Here, we provide a generalized Hatano-Nelson model with higher-order nonreciprocal hoppings, non-Abelian gauge fields, and staggered gain-loss processes showing the exceptional topological structure of the Hopf-link braids that undergoes a EP-mediated topological phase transition. We demonstrate that mixing multiple nonreciprocal channels drives the system into highly intricate, nested complex energy Hopf-link braids and expands the topological landscape up to higher-order braiding sectors. Furthermore, utilizing biorthogonal eigenvector tracking, we map the structural evolution of the exceptional phase boundaries via the maximum Petermann factor in the phase angle parameter planes. We show that the gain-loss non-Hermiticity drives a topological crossover where the extended exceptional contours constrict into isolated regimes. The demonstration of EP-mediated topological phase transition of Hopf-link braids and the associated rich exceptional phase portraits may offer new physical insights with promising applications in robust, fault-tolerant communication channels and quantum computing platforms.
Related
- Non-Hermitian exceptional topology on a Klein bottle photonic circuit
- Photonic Exceptional Topological Bound States in the Continuum
- Topological localization in unentangled random braids
- Controlling exceptional points of layered non-Hermitian structures with magnetic field
- Non-Hermitian Rayleigh-Schrödinger-like perturbation theory at exceptional point
BibTeX
@misc{gupta2026exceptional,
title = {{Exceptional Topological Signatures of Non-Hermitian Photonic Hopf-Link Braids}},
author = {Samit Kumar Gupta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02589},
eprint = {2609.02589},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02589},
}
RIS
TY - UNPB
TI - Exceptional Topological Signatures of Non-Hermitian Photonic Hopf-Link Braids
AU - Samit Kumar Gupta
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02589
UR - https://arxiv.org/abs/2609.02589
AB - Non-Hermitian physics endows the non-Abelian systems with exceptional topology characterized by non-commutative braid patterns. Interplay of distinct competing sources of non-Hermiticity may induce novel topological effects. Here, we provide a generalized Hatano-Nelson model with higher-order nonreciprocal hoppings, non-Abelian gauge fields, and staggered gain-loss processes showing the exceptional topological structure of the Hopf-link braids that undergoes a EP-mediated topological phase transition. We demonstrate that mixing multiple nonreciprocal channels drives the system into highly intricate, nested complex energy Hopf-link braids and expands the topological landscape up to higher-order braiding sectors. Furthermore, utilizing biorthogonal eigenvector tracking, we map the structural evolution of the exceptional phase boundaries via the maximum Petermann factor in the phase angle parameter planes. We show that the gain-loss non-Hermiticity drives a topological crossover where the extended exceptional contours constrict into isolated regimes. The demonstration of EP-mediated topological phase transition of Hopf-link braids and the associated rich exceptional phase portraits may offer new physical insights with promising applications in robust, fault-tolerant communication channels and quantum computing platforms.
ER -