Emergent gauge field for a chiral bound state on curved surface

Emergent physics is one of the most important concepts in modern physics, and one of the most intriguing examples is the emergent gauge field. Here we show that a gauge field emerges for a chiral bound state formed by two attractively interacting particles on a curved surface. We demonstrate explicitly that the center-of-mass wave function of such a deeply bound state is monopole harmonic instead of spherical harmonic, which means that the bound state experiences a magnetic monopole at the center of the sphere. This emergent gauge field is due to the coupling between the center-of-mass and the relative motion on a curved surface, and our results can be generalized to an arbitrary curved surface. This result establishes an intriguing connection between the space curvature and gauge field, and paves an alternative way to engineer a topological state with space curvature, and may be observed in a cold atom system.