Synthetic half-integer magnetic monopole and single-vortex dynamics in spherical Bose-Einstein condensates

Magnetic monopoles are crucial in explaining the quantization of electric charges and quantum Hall effects, while artificially creating a minimal magnetic monopole in experiments remains a challenge. Here, we come up with a flexible way to simulate a half-integer-type monopole in Bose gases and investigate the induced vortex dynamics on a sphere. We list the possible experiment parameter settings for different isotopes and discuss their experimental feasibility. With the assumption of a rigid monopole-vortex structure, we analytically predict the vortex trajectory in an external magnetic field. We then confirm the result by numerically solving the Gross-Pitaevskii equation, which employs two gauges simultaneously (the Wu-Yang approach) to prevent singularity in the one-gauge method when a monopole is present. The study offers significant insight into the characteristics of monopoles and vortices, facilitating avenues for experimental validation.