Measuring non-Abelian quantum geometry and topology in a multi-gap photonic lattice
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| Main Authors: | , , , , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917390679277568 |
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| author | Guillot, Martin Blanchard, Cédric Morassi, Martina Lemaître, Aristide Gratiet, Luc Le Harouri, Abdelmounaim Sagnes, Isabelle Slager, Robert-Jan Ünal, F. Nur Bloch, Jacqueline Ravets, Sylvain |
| author_facet | Guillot, Martin Blanchard, Cédric Morassi, Martina Lemaître, Aristide Gratiet, Luc Le Harouri, Abdelmounaim Sagnes, Isabelle Slager, Robert-Jan Ünal, F. Nur Bloch, Jacqueline Ravets, Sylvain |
| contents | Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of topological phases necessitates novel approaches to probe them in laboratories, a pursuit that intricately relates to evaluating non-Abelian generalizations of the Abelian quantum geometric tensor (QGT) that characterizes geometric responses. Here, we pioneer the direct measurement of the non-Abelian QGT. We achieve this by implementing a novel orbital-resolved polarimetry technique to probe the full Bloch Hamiltonian of a six-band two-dimensional (2D) synthetic lattice, which grants direct experimental access to non-Abelian quaternion charges, the Euler curvature, and the non-Abelian quantum metric associated with all bands. Quantum geometry has been highlighted to play a key role on macroscopic phenomena ranging from superconductivity in flat-bands, to optical responses, transport, metrology, and quantum Hall physics. Therefore, our work unlocks the experimental probing of a wide phenomenology of multi-gap systems, at the confluence of topology, geometry and non-Abelian physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03894 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measuring non-Abelian quantum geometry and topology in a multi-gap photonic lattice Guillot, Martin Blanchard, Cédric Morassi, Martina Lemaître, Aristide Gratiet, Luc Le Harouri, Abdelmounaim Sagnes, Isabelle Slager, Robert-Jan Ünal, F. Nur Bloch, Jacqueline Ravets, Sylvain Mesoscale and Nanoscale Physics Quantum Gases Optics Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of topological phases necessitates novel approaches to probe them in laboratories, a pursuit that intricately relates to evaluating non-Abelian generalizations of the Abelian quantum geometric tensor (QGT) that characterizes geometric responses. Here, we pioneer the direct measurement of the non-Abelian QGT. We achieve this by implementing a novel orbital-resolved polarimetry technique to probe the full Bloch Hamiltonian of a six-band two-dimensional (2D) synthetic lattice, which grants direct experimental access to non-Abelian quaternion charges, the Euler curvature, and the non-Abelian quantum metric associated with all bands. Quantum geometry has been highlighted to play a key role on macroscopic phenomena ranging from superconductivity in flat-bands, to optical responses, transport, metrology, and quantum Hall physics. Therefore, our work unlocks the experimental probing of a wide phenomenology of multi-gap systems, at the confluence of topology, geometry and non-Abelian physics. |
| title | Measuring non-Abelian quantum geometry and topology in a multi-gap photonic lattice |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Optics |
| url | https://arxiv.org/abs/2511.03894 |