Experimental Realization of Non-Abelian Permutations in a Three-State Non-Hermitian System

TL;DR

This paper reports the first experimental demonstration of non-Abelian permutations in a three-state non-Hermitian system, revealing complex state evolutions and exotic winding effects through encircling exceptional arcs.

Contribution

It introduces a novel experimental method to realize and confirm non-Abelian state permutations in a non-Hermitian system using exceptional arc encirclements.

Findings

Five non-trivial permutations realized experimentally

Confirmed non-Abelian characteristics through sequence-dependent encircling

Provides a new platform for studying exotic topological effects in non-Hermitian systems

Abstract

Eigenstates of a non-Hermitian system exist on complex Riemannian manifolds, with multiple sheets connecting at branch cuts and exceptional points (EPs). These eigenstates can evolve across different sheets, a process that naturally corresponds to state permutation. Here, we report the first experimental realization of non-Abelian permutations in a three-state non- Hermitian system. Our approach relies on the stroboscopic encircling of two different exceptional arcs (EAs), which are smooth trajectories of order-2 EPs appearing from the coalescence of two adjacent states. The non-Abelian characteristics are confirmed by encircling the EAs in opposite sequences. A total of five non-trivial permutations are experimentally realized, which together comprise a non-Abelian group. Our approach provides a reliable way of investigating non-Abelian state permutations and the related exotic winding effects in non- Hermitian systems.