Optical excitations of Skyrmions, knotted solitons, and defects in atoms

Abstract Analogies between non-trivial topologies of matter and light have inspired numerous studies, including defect formation in structured topological photonic band structures. Three-dimensional objects localised particle-like nature attract broad interest across discipline boundaries from elementary particle physics cosmology to condensed physics. Here we propose how simple beams can be transformed into optical excitations atoms with considerably more complex representing three-dimensional Skyrmions. This construction also described terms linked Hopf maps, analogous knotted solitons the Skyrme-Faddeev model. We identify transverse polarisation density current as effective magnetic gauge potential for Chern-Simons helicity term. While prepare simpler two-dimensional baby-Skyrmions singular defects using traditional Stokes vectors on Poincaré sphere light, only achieved full hypersphere description that no longer discards variation total electromagnetic phase vibration.