Experimental realization of non-Abelian permutations in a three-state non-Hermitian system

Weiyuan Tang; Kun Ding; Guancong Ma

doi:10.1093/nsr/nwac010

Experimental realization of non-Abelian permutations in a three-state non-Hermitian system

Natl Sci Rev. 2022 Jan 18;9(11):nwac010. doi: 10.1093/nsr/nwac010. eCollection 2022 Nov.

Authors

Weiyuan Tang¹, Kun Ding², Guancong Ma¹

Affiliations

¹ Department of Physics, Hong Kong Baptist University, Hong Kong, China.
² Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai200438, China.

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.

Keywords: acoustics; non-Abelian permutation; non-Hermitian physics; topological physics.