Topological Matter and Fractional Entangled Quantum Geometry through Light

• URL: http://arxiv.org/abs/2209.15381v5
• Date: Sat, 2 Sep 2023 06:47:15 GMT
• Title: Topological Matter and Fractional Entangled Quantum Geometry through Light
• Authors: Karyn Le Hur
• Abstract summary: We show that global topological properties are encoded from the poles of the surface allowing a correspondence between smooth fields, metric and quantum distance with the square of the topological number. We develop the theory, "quantum topometry" in space and time, and present applications on transport from a Newtonian approach.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2 particle acquires an integer topological charge in the presence of a radial magnetic field. We show that global topological properties are encoded from the poles of the surface allowing a correspondence between smooth fields, metric and quantum distance with the square of the topological number. The information is transported from each pole to the equatorial plane on a thin Dirac string. We develop the theory, "quantum topometry" in space and time, and present applications on transport from a Newtonian approach, on a quantized photo-electric effect from circular dichroism of light towards topological band structures of crystals. Edge modes related to topological lattice models are resolved analytically when deforming the sphere or ellipse onto a cylinder. Topological properties of the quantum Hall effect, quantum anomalous Hall effect and quantum spin Hall effect on the honeycomb lattice can be measured locally in the Brillouin zone from light-matter coupling. The formalism allows us to include interaction effects from the momentum space. Interactions may also result in fractional entangled geometry within the curved space. We develop a relation between entangled wavefunction in quantum mechanics, coherent superposition of geometries, a way to one-half topological numbers and Majorana fermions. We show realizations in topological matter. We present a link between axion electrodynamics, topological insulators on a surface of a cube and the two-spheres' model via merons.

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