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

Resting on the novel non-Hermitian topology, we experimentally demonstrate state permutations in a non-Hermitian system follow non-Abelian, or order-dependent exchange rules. 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.

Automated summary

In this study, non-Abelian state permutations are experimentally demonstrated in a non-Hermitian system. The eigenstates in this system can evolve across different manifolds, corresponding to state permutation. By encircling exceptional arcs, five non-trivial permutations are achieved, indicating the existence of non-Abelian groups in non-Hermitian systems.