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

Christopher D Parmee,Mark R Dennis,Janne Ruostekoski

doi:10.1038/s42005-022-00829-y

Christopher D Parmee, Mark R Dennis + Show 1 more

Open Access

https://doi.org/10.1038/s42005-022-00829-y

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Abstract

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

Highlights

Analogies between non-trivial topologies of matter and light have inspired numerous studies, including defect formation in structured light and topological photonic band structures
Non-trivial defects, textures, and knots have inspired physicists since the days of Kelvin[1]. They are remarkably ubiquitous throughout physics, spanning a vast range of energy scales from cosmology and elementary particle physics, to superconductors, superfluidity, and liquid crystals
By going beyond the Stokes representation of light beams to incorporate the full degrees of freedom of the complex field amplitudes, where we no longer discard the spatial variation of the sum of the phases for the two field components, we can form 3D particle-like Skyrmions, localised in space

Summary

Introduction

Analogies between non-trivial topologies of matter and light have inspired numerous studies, including defect formation in structured light and topological photonic band structures. The experimental study of topological defects and textures in structured optical fields has emerged as one of the most promising areas to engineer and detect topologically nontrivial characteristics[3], including singularities of the phase or polarisation that may form knotted or linked geometries[4–7] or Möbius strips[8] Another line of research on non-trivial topologies of light has focused on photonic band structures[9], analogous to electronic band structures in crystals. We identify the transverse polarisation density of the atoms as a synthetic magnetic vector potential of the 3D Skyrmions with non-trivial helicity While constructing such an object directly in a light beam is quite challenging even for modern structured light engineering[33], we show how appropriately adjusting the light-matter coupling provides a solution with simple copropagating beams. These behave as spatially delocalised “superatoms”, exhibiting their own collective resonance linewidth and line shift

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