Designing Yang-Mills topological vacua with cold atoms

Topological vacua are a family of degenerate ground states of Yang-Mills fields with zero field strength but non-trivial topological structures. They play a fundamental role in particle physics and quantum field theory but have not yet been experimentally observed. Here, we propose an experimental scheme to realize 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 supporting 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, distinct from the electromagnetic case, persist even with vanishing gauge field strengths throughout space.