Skyrmionic SU(6) structured light

Skyrmions are topological quasi-particles characterised by local spin textures, which are considered to be robust against structural deformation. N\'eel and Bloch states are famous examples of skyrmions, which exhibit radical and chiral spin profiles, respectively. Here, we show a skyrmion can be continuously transformed to an antiskyrmion or various other forms of skymions through underlying symmetry of special unitary group of degree six, SU(6), for photons with spin and orbital angular momentum. We employ a Lie group theory for coherent photons to describe the SU(6) transformation and establish a relationship between the generator of rotation and its expectation values on a hypersphere of $\mathbb{S}^{35}$. We propose a simple experimental setup to control the SU(6) states in combinations with wave-plates and vortex lenses to realise the generalised Euler's formula physically in a Mach-Zehnder interferometer. We show skyrmionic states are described on higher-order Poincar'e spheres together with a recently proposed skyrmionic torus.