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Fibonacci Waveguide Quantum Electrodynamics

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Fibonacci Waveguide Quantum Electrodynamics

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AbstractWaveguide quantum electrodynamics (QED) provides a powerful framework for engineering quantum interactions, traditionally relying on periodic photonic arrays with continuous energy bands. Here, we investigate waveguide QED in a fundamentally different environment: A one-dimensional photonic array whose hopping strengths are structured aperiodically according to the deterministic Fibonacci-Lucas substitution rule. These "Fibonacci waveguides" lack translational invariance and are characterized by a singular continuous energy spectrum and critical eigenstates, representing a deterministic intermediate between ordered and disordered systems. We demonstrate how to achieve decoherence-free, coherent interactions in this unique setting. We analyze two paradigmatic cases: (i) Giant emitters resonantly coupled to the simplest aperiodic version of a standard waveguide. For these, we show that atom photon bound states form only for specific coupling configurations dictated by the aperiodic sequence, leading to an effective atomic Hamiltonian, which itself inherits the Fibonacci structure; and (ii) emitters locally and off-resonantly coupled to the aperiodic version of the Su-Schrieffer-Heeger waveguide. In this case the mediating bound states feature aperiodically modulated profiles, resulting in an effective Hamiltonian with multifractal properties. Our work establishes Fibonacci waveguides as a versatile platform, which is experimentally feasible, demonstrating that the deterministic complexity of aperiodic structures can be directly engineered into the interactions between quantum emitters.Featured image: Fibonacci waveguides imprint multifractality onto atom-photon bound states and the decoherence-free interaction mediated by them.Popular summaryFibonacci waveguides utilize the deterministic Fibonacci-Lucas substitution rule to structure hopping strengths, representing an alternative to standard periodic photonic arrays. These systems inhabit a unique regime between perfect order and total randomness, defined by singular continuous energy spectra and critical eigenstates that are neither fully extended nor exponentially localized. We demonstrate decoherence-free, coherent interactions within this aperiodic environment. Through the employment of multi-local giant emitters or off-resonant local atoms, the resulting atom-photon bound states inherit the mathematical complexity of the underlying lattice. This imprinting allows the aperiodic structure to dictate the dynamics of the emitters directly, offering a versatile platform for engineering complex quantum interactions and simulating physics beyond standard periodic structures.► BibTeX data@article{Bonsel2026fibonacciwaveguide, doi = {10.22331/q-2026-04-23-2081}, url = {https://doi.org/10.22331/q-2026-04-23-2081}, title = {Fibonacci {W}aveguide {Q}uantum {E}lectrodynamics}, author = {B{\"{o}}nsel, Florian and Kunst, Flore K. and Roccati, Federico}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2081}, month = apr, year = {2026} }► References [1] Ramachandrarao Yalla, Mark Sadgrove, Kali P. Nayak, and Kohzo Hakuta. ``Cavity quantum electrodynamics on a nanofiber using a composite photonic crystal cavity''. Physical review letters 113, 143601 (2014). https://doi.org/10.1103/PhysRevLett.113.143601 [2] A. Goban, C.-L. Hung, S.-P. Yu, J.D. Hood, J.A. Muniz, J.H. Lee, M.J. Martin, A.C. McClung, K.S. Choi, Darrick E. Chang, et al. ``Atom–light interactions in photonic crystals''. Nature communications 5, 3808 (2014). https://doi.org/10.1038/ncomms4808 [3] Andreas Albrecht, Loïc Henriet, Ana Asenjo-Garcia, Paul B. Dieterle, Oskar Painter, and Darrick E. Chang. ``Subradiant states of quantum bits coupled to a one-dimensional waveguide''. New Journal of Physics 21, 025003 (2019). https://doi.org/10.1088/1367-2630/ab0134 [4] Janos Perczel, Johannes Borregaard, Darrick E. Chang, Hannes Pichler, Susanne F. Yelin, Peter Zoller, and Mikhail D. Lukin. ``Topological quantum optics in two-dimensional atomic arrays''. Physical review letters 119, 023603 (2017). https://doi.org/10.1103/PhysRevLett.119.023603 [5] Alexandra S. Sheremet, Mihail I. Petrov, Ivan V. Iorsh, Alexander V. Poshakinskiy, and Alexander N. Poddubny. ``Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations''. Reviews of Modern Physics 95, 015002 (2023). https://doi.org/10.1103/RevModPhys.95.015002 [6] Francesco Ciccarello, Peter Lodahl, and Dominik Schneble. ``Waveguide quantum electrodynamics''. Optics and Photonics News 35, 34–41 (2024). https://doi.org/10.1364/OPN.35.1.000034 [7] Xin Wang, Jia-Qi Li, Tao Liu, Adam Miranowicz, and Franco Nori. ``Long-range four-body interactions in structured nonlinear photonic waveguides''.

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Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWaveguide quantum electrodynamics (QED) provides a powerful framework for engineering quantum interactions, traditionally relying on periodic photonic arrays with continuous energy bands. Here, we investigate waveguide QED in a fundamentally different environment: A one-dimensional photonic array whose hopping strengths are structured aperiodically according to the deterministic Fibonacci-Lucas substitution rule. These "Fibonacci waveguides" lack translational invariance and are characterized by a singular continuous energy spectrum and critical eigenstates, representing a deterministic intermediate between ordered and disordered systems. We demonstrate how to achieve decoherence-free, coherent interactions in this unique setting. We analyze two paradigmatic cases: (i) Giant emitters resonantly coupled to the simplest aperiodic version of a standard waveguide. For these, we show that atom photon bound states form only for specific coupling configurations dictated by the aperiodic sequence, leading to an effective atomic Hamiltonian, which itself inherits the Fibonacci structure; and (ii) emitters locally and off-resonantly coupled to the aperiodic version of the Su-Schrieffer-Heeger waveguide. In this case the mediating bound states feature aperiodically modulated profiles, resulting in an effective Hamiltonian with multifractal properties. Our work establishes Fibonacci waveguides as a versatile platform, which is experimentally feasible, demonstrating that the deterministic complexity of aperiodic structures can be directly engineered into the interactions between quantum emitters.Featured image: Fibonacci waveguides imprint multifractality onto atom-photon bound states and the decoherence-free interaction mediated by them.Popular summaryFibonacci waveguides utilize the deterministic Fibonacci-Lucas substitution rule to structure hopping strengths, representing an alternative to standard periodic photonic arrays. These systems inhabit a unique regime between perfect order and total randomness, defined by singular continuous energy spectra and critical eigenstates that are neither fully extended nor exponentially localized. We demonstrate decoherence-free, coherent interactions within this aperiodic environment. Through the employment of multi-local giant emitters or off-resonant local atoms, the resulting atom-photon bound states inherit the mathematical complexity of the underlying lattice. This imprinting allows the aperiodic structure to dictate the dynamics of the emitters directly, offering a versatile platform for engineering complex quantum interactions and simulating physics beyond standard periodic structures.► BibTeX data@article{Bonsel2026fibonacciwaveguide, doi = {10.22331/q-2026-04-23-2081}, url = {https://doi.org/10.22331/q-2026-04-23-2081}, title = {Fibonacci {W}aveguide {Q}uantum {E}lectrodynamics}, author = {B{\"{o}}nsel, Florian and Kunst, Flore K. and Roccati, Federico}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2081}, month = apr, year = {2026} }► References [1] Ramachandrarao Yalla, Mark Sadgrove, Kali P. 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Fibonacci Waveguide Quantum Electrodynamics

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