- Letter
Index theorem and vortex kinetics in Bose-Einstein condensates on a Haldane sphere with a magnetic monopole
Phys. Rev. A 113, L041304 – Published 13 April, 2026
DOI: https://doi.org/10.1103/2msv-lk1m
Abstract
Geometry-gauge interplay constitutes a fundamental issue in quantum physics, with profound implications spanning from quantum gravity to topological matter. Here we investigate the dynamic effects of geometry-gauge interplay in Bose-Einstein condensates on a Haldane sphere with a magnetic monopole. We reveal an index theorem that links vortex configurations to the topology of the gauge field, enabling the construction of vortex-monopole composites. Furthermore, we derive the universal logarithmic interaction between composites, which governs the structure of the ground-state vortex lattice. By developing a kinetic theory, we predict scale-invariant vortex dynamics and an emergent dynamical correspondence between vortex-vortex and vortex-antivortex systems. Both are confirmed through numerical simulations. This work uncovers a dynamical coupling mechanism between spatial geometry and gauge fields, providing deep insights into superfluid systems with topological gauge structures in curved space.
