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Topology and Spectral Entanglement in Cavity-Mediated Photon Scattering
Eric R. Bittner, Andrei Piryatinski
https://arxiv.org/abs/2509.15465 https://arxiv.…

Topology and Spectral Entanglement in Cavity-Mediated Photon Scattering
We develop a diagrammatic theory of cavity-mediated photon-photon interactions in a topological insulator using the SSH model. The fourth-order vertex $Γ^{(4)}(ω_1,ω_2)$ governs spectral entanglement and Kerr nonlinearity, leading to a nonlinear topological phase diagram. We also compute the electronic self-energy from vacuum photon exchange and identify symmetry-imposed limits on band renormalization. These results link band geometry to the emergence of light-matter correlations.