Monopoles Constructed by Cold Atoms*

Monopoles are important topological structures in many important areas in physics. In the last few years, cold atom experiments are able to simulated both Dirac monopoles and Yang Monopoles, which appear in the manifold of non-degenerate ground states and degenerate ground states, are characterized by non-vanishing first and second Chern numbers respectively. Motivated by the recent experiment at NIST (arXiv:1610.06228) on Yang monopole constructed by ⁸⁷Rb, we have studied how interactions between atoms affect these Chern numbers. We show that without quantum fluctuation, interaction will stretch the monopole into an extended manifold of singularity in the parameter space. With quantum fluctuation, the singular manifold is transformed into volume of fragmented condensate. The interaction effect will cause a gradual change of Chern numbers as a monopole leaves the closed surface where Chern numbers are calculated. The interaction effect is contained in the data of the NIST experiment.