Fibonacci Waveguide Quantum Electrodynamics

Bönsel F, Kunst FK, Roccati F (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Quantum Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften e-V-

Journal Issue: 10

DOI: 10.22331/q-2026-04-23-2081

Abstract

Waveguide 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.

Involved external institutions

Max-Planck-Institut für die Physik des Lichts (MPL) / Max Planck Institute for the Science of Light DE Germany (DE)

How to cite

APA:

Bönsel, F., Kunst, F.K., & Roccati, F. (2026). Fibonacci Waveguide Quantum Electrodynamics. Quantum, 10. https://doi.org/10.22331/q-2026-04-23-2081

MLA:

Bönsel, Florian, Flore K. Kunst, and Federico Roccati. "Fibonacci Waveguide Quantum Electrodynamics." Quantum 10 (2026).

BibTeX: Download