Designing Yang–Mills Topological Vacua with Cold Atoms

Abstract Topological vacua, a family of degenerate ground states of the Yang–Mills fields with zero field strength but nontrivial topological structures, play a fundamental role in particle physics and quantum field theory. However, they have not yet been experimentally observed. Here, we propose an experimental scheme to realize a real-space SU(2) artificial Yang–Mills topological vacua using a cloud of two-Λ-level cold atoms. We derive analytical expressions for the gauge transformations and gauge potentials of these topological vacua. Specifically, we propose a degenerate subspace that supports Yang–Mills gauge fields and identify the laser configurations required to realize the topological vacua. Furthermore, we generalize the vacua to a family with a topological number given by the product of two integers. We also propose an Aharonov–Bohm interference experiment to detect the resulting geometric phases, which persist even with vanishing gauge field strengths throughout space, distinct from the electromagnetic case.