FAU LMQ Research Spotlight: Harnessing Fibonacci Patterns To Engineer Light-Matter Interactions

Controlling how artificial atoms “talk” to each other is important for building advanced quantum technologies. Traditionally, scientists have guided these interactions using perfectly ordered, periodic structures, like a crystal lattice. This approach, however, limits the complexity of the quantum systems that can be engineered.

In a recent publication, researchers from the Max Planck Institute for the Science of Light, Friedrich-Alexander-Universität Erlangen-Nürnberg, and the Università degli Studi di Palermo have tried a new path. They proposed a photonic waveguide — a data bus for light — structured not with simple repetition, but according to the quasi-periodic Fibonacci sequence. This creates a unique platform between the predictability of a crystal and the randomness of a disordered system.

They discovered that in this special waveguide, the interactions between atoms, mediated by photons, become highly selective. Multilocal (so-called ‘giant’) atoms for example together with photons can only form stationary “bound states” at specific locations dictated by the underlying Fibonacci pattern.

This selectivity allows the complexity of the Fibonacci sequence to be directly imprinted onto the network of interacting atoms. The result is a quantum system with unique, long-range interactions that exhibit „multifractal” properties with a rich structure at larger scales. The work establishes Fibonacci waveguides as a versatile and experimentally feasible platform, providing a novel toolkit for creating and exploring complex quantum systems.