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<p>Skyrmions are topological quasi-particles with local spin textures, which are considered to be robust against structural deformation. Néel 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 states with unique spin textures through the underlying symmetry of the 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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_2344_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\mathbb{S}}}^{35}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">S</mi> </mrow> <mrow> <mn>35</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>. 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 that skyrmionic states are described on higher-order Poincaré spheres together with a recently proposed skyrmionic torus.</p>

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Skyrmionic textures within SU(6) structured light

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  • 发表日期：

    2025年11月17日

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  • Shinichi Saito

摘要

Skyrmions are topological quasi-particles with local spin textures, which are considered to be robust against structural deformation. Néel 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 states with unique spin textures through the underlying symmetry of the 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 \({{\mathbb{S}}}^{35}\) 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 that skyrmionic states are described on higher-order Poincaré spheres together with a recently proposed skyrmionic torus.