Atom-Photon Bound States in Fractal Photonic Lattices: Localization Length and Anomalous Diffusion

• URL: http://arxiv.org/abs/2605.23625v1
• Date: Fri, 22 May 2026 13:33:05 GMT
• Title: Atom-Photon Bound States in Fractal Photonic Lattices: Localization Length and Anomalous Diffusion
• Abstract summary: We study atom-photon bound states seeded by two-level emitters coupled to self-similar photonic lattices.<n>We show that the far-field localization length obeys $sim -1/d_w$, with the detuning $$ from the lower spectral edge.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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