Atom-Photon Bound States in Fractal Photonic Lattices: Localization Length and Anomalous Diffusion
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arXiv
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| Format: | Preprint |
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2026
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| author | Bönsel, Florian Kunst, Flore K. Roccati, Federico |
| author_facet | Bönsel, Florian Kunst, Flore K. Roccati, Federico |
| contents | We study atom-photon bound states seeded by two-level emitters coupled to self-similar photonic lattices. By expressing the photonic Green's function through the heat kernel, we show that the far-field localization length obeys $ξ\sim Δ^{-1/d_w}$, with the detuning $Δ$ from the lower spectral edge and the walk dimension $d_w$ of the underlying fractal. This scaling is controlled by anomalous diffusion and does not rely on translational invariance or a band-edge effective-mass approximation. Exact diagonalization on Sierpiński gaskets, pyramids, Vicsek graphs, and Sierpiński carpets confirms the far-field prediction once the bath Hamiltonian is rendered Laplacian-like by compensating the local inhomogeneity in the connectivities with on-site potentials. In the near field, the bound-state amplitude exhibits an additional algebraic variation. For nested finitely ramified fractals, the corresponding exponent agrees with the classical resistance/ first-passage scaling, whereas Sierpiński carpets display clear deviations from this simple law. Our results extend structured-bath waveguide QED to self-similar non-periodic geometries and connect bound-state profiles to transport exponents of the underlying fractal lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23625 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Atom-Photon Bound States in Fractal Photonic Lattices: Localization Length and Anomalous Diffusion Bönsel, Florian Kunst, Flore K. Roccati, Federico Quantum Physics Mesoscale and Nanoscale Physics Optics We study atom-photon bound states seeded by two-level emitters coupled to self-similar photonic lattices. By expressing the photonic Green's function through the heat kernel, we show that the far-field localization length obeys $ξ\sim Δ^{-1/d_w}$, with the detuning $Δ$ from the lower spectral edge and the walk dimension $d_w$ of the underlying fractal. This scaling is controlled by anomalous diffusion and does not rely on translational invariance or a band-edge effective-mass approximation. Exact diagonalization on Sierpiński gaskets, pyramids, Vicsek graphs, and Sierpiński carpets confirms the far-field prediction once the bath Hamiltonian is rendered Laplacian-like by compensating the local inhomogeneity in the connectivities with on-site potentials. In the near field, the bound-state amplitude exhibits an additional algebraic variation. For nested finitely ramified fractals, the corresponding exponent agrees with the classical resistance/ first-passage scaling, whereas Sierpiński carpets display clear deviations from this simple law. Our results extend structured-bath waveguide QED to self-similar non-periodic geometries and connect bound-state profiles to transport exponents of the underlying fractal lattice. |
| title | Atom-Photon Bound States in Fractal Photonic Lattices: Localization Length and Anomalous Diffusion |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Optics |
| url | https://arxiv.org/abs/2605.23625 |