Emergent Gauge Field for a Chiral Bound State on Curved Surface

In this letter we show that there emerges a gauge field for two attractive particles moving on a curved surface when they form a chiral bound state. By solving a two-body problem on a sphere, we show explicitly that the center-of-mass wave functions of such deeply bound states are monopole harmonics instead of spherical harmonics. This indicates that the bound state experiences a gauge field identical to a magnetic monopole at the center of the sphere, with the monopole charge equal to the quantized relative angular momentum of this bound state. We show that this emergent gauge field is due to the coupling between the center-of-mass and the relative motion on curved surfaces. Our results can be generalized to an arbitrary curved surface where the emergent magnetic field is exactly the local Gaussian curvature. This result establishes an intriguing connection between space curvature and gauge field, paves an alternative way to engineer topological state with space curvature, and may be observed in cold atom system.