Experimental realization of non-Abelian gauge field in circuit system

Abstract Synthetic gauge field, especially the non-Abelian gauge field, has emerged as a new way to explore exotic physics in a wide range of materials and platforms. Here we present the building blocks, consisting of capacitors and inductors, to implement the non-Abelian tunneling matrices and show that circuit system is an appropriate choice to realize the non-Abelian gauge field. To demonstrate the novel physics enabled by the non-Abelian gauge field, we provide a simple and modular scheme to design the Rashba-Dresselhaus spin-orbit interaction and topological Chern state in circuits. By measuring the spin texture and chiral edge states of the resonant frequency band structures, we confirm the spin-orbit effect and topological Chern state in circuits. Our schemes open a broad avenue to study non-Abelian gauge field and related physics in circuit platform.