Synthetic non-Abelian topological charges in ultracold atomic gases

TL;DR

This paper proposes a theoretical method to synthesize non-Abelian quaternion topological charges in ultracold atomic gases, enabling the study of their unique bulk-edge correspondence and interface modes with current experimental techniques.

Contribution

It introduces a novel framework for creating non-Abelian quaternion charges in ultracold gases through artificial spin-orbit coupling, linking topological edge modes with quaternion band topology.

Findings

Demonstrates a clear bulk-edge correspondence for non-Abelian charges.

Proposes a feasible implementation using existing ultracold atom technology.

Highlights the fundamental role of nonconservation multiplication in interface modes.

Abstract

Topological phases associated with non-Abelian charges can exhibit a distinguished bulk-edge correspondence compared with Abelian phases, although elucidating this relationship remains challenging in traditional solid-state systems. In this paper, we propose a theoretical framework for synthesizing non-Abelian quaternion charges in ultracold atomic gases. By designing artificial spin-orbit coupling patterns, the topological edge modes demonstrate a clear correspondence with the band topology determined by various quaternion charges. This paves the way for observing the interface modes whose existence is attributed to the nonconservation multiplication relation, which is fundamental to non-Abelian charges. This scheme can be readily implemented using current ultracold atom techniques, offering a promising approach to explore the intriguing non-Abelian characteristics of the system.