Mainz 2026 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 28: Poster – Quantum Optics
Q 28.2: Poster
Dienstag, 3. März 2026, 17:00–19:00, Philo 2. OG
Fractal geometry dictates the scaling of atom-photon bound states — •Florian Bönsel1,2, Federico Roccati1,3, and Flore Kunst1,2 — 1Max Planck Institute for the Science of Light, 91058 Erlangen, Germany — 2Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany — 3Dipartimento di Fisica e Chimica - Emilio Segre, Universita degli Studi di Palermo, I-90123 Palermo, Italy
We investigate the formation of atom-photon bound states in self-similar photonic lattices and derive a universal scaling law linking the localization length to the atom-bath detuning. By utilizing the heat-kernel representation of the Green’s function, we circumvent the momentum-based approaches standard in waveguide QED. A key finding is that the scaling exponent is governed solely by the walk dimension, which characterizes classical anomalous diffusion, rather than the fractal or spectral dimension. This establishes a novel link between static quantum localization and dynamical transport. Numerical simulations on several fractals, such as Sierpinski and Vicsek graphs, confirm the derived results.
Keywords: fractals; waveguide; bound states; quantum emitters