Fibonacci Waveguide Quantum Electrodynamics

TL;DR

This paper explores waveguide quantum electrodynamics in Fibonacci-structured photonic arrays, revealing unique spectral properties and enabling decoherence-free quantum interactions through engineered aperiodic structures.

Contribution

It introduces Fibonacci waveguides as a new platform for quantum interactions, demonstrating how aperiodic order influences bound states and effective Hamiltonians.

Findings

Fibonacci waveguides have a singular continuous energy spectrum.

Atom-photon bound states form only at specific coupling configurations.

Effective Hamiltonians inherit Fibonacci or multifractal properties.

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.