Synthetic Non-Abelian Gauge Fields for Non-Hermitian Systems

Abstract

<p>Non-Abelian gauge fields are versatile tools for synthesizing topological phenomena, but have so far<br>been mostly studied in Hermitian systems, where gauge flux has to be defined from a closed loop in order<br>for vector potentials, whether Abelian or non-Abelian, to become physically meaningful.We show that this<br>condition can be relaxed in non-Hermitian systems by proposing and studying a generalized Hatano-<br>Nelson model with imbalanced non-Abelian hopping. Despite lacking gauge flux in one dimension, non-<br>Abelian gauge fields create rich non-Hermitian topological consequences. With SU(2) gauge fields, the<br>braiding degrees that can be achieved are twice the highest hopping order of a lattice model, indicating the<br>utility of spinful freedom to attain high-order nontrivial braiding. At both ends of an open chain, non-<br>Abelian gauge fields lead to the simultaneous presence of non-Hermitian skin modes, whose population<br>can be effectively tuned near the exceptional points. Generalizing to two dimensions, the gauge invariance<br>of Wilson loops can also break down in non-Hermitian lattices dressed with non-Abelian gauge fields.<br>Toward realization, we present a concrete experimental proposal for non-Abelian gauge fields in non-<br>Hermitian systems via the synthetic frequency dimension of a polarization-multiplexed fiber ring resonator.</p>