Non-abelian gauge fields in circuit systems

TL;DR

This paper demonstrates the synthesis of non-Abelian gauge fields in electrical circuits using basic components, enabling the exploration of complex topological phenomena and non-reciprocal effects in a controllable platform.

Contribution

It introduces a method to realize non-Abelian gauge fields in circuits with capacitors, inductors, and resistors, facilitating studies of topological states and gauge effects.

Findings

Created circuit designs for spin-orbit interaction and Chern states.

Implemented non-Abelian Aharonov-Bohm effect in circuits.

Enabled exploration of topological phenomena in circuit systems.

Abstract

Circuits can provide a platform to study novel physics and have been used, for example, to explore various topological phases. Gauge fields-particularly, non-Abelian gauge fields-can play a pivotal role in the design and modulation of novel physical states, but their circuit implementation has so far been limited. Here we show that non-Abelian gauge fields can be synthesized in circuits created from building blocks that consist of capacitors, inductors and resistors. With these building blocks, we create circuit designs for the spin-orbit interaction and the topological Chern state, which are phenomena that represent non-Abelian gauge fields in momentum space. We also use the approach to design non-reciprocal circuits that can be used to implement the non-Abelian Aharonov-Bohm effect in real space.