Synthesising multi-dimensional excitation dynamics and localisation transition in one-dimensional lattices

Abstract

The excitation dynamics in complex networks1 can describe the fundamental aspects of transport and localization across multiple fields of science, ranging from solid-state physics and photonics to biological signalling pathways and neuromorphic circuits2,3,4,5. Although the effects of increasing network dimensionality are highly non-trivial, their implementation likewise becomes ever more challenging due to the exponentially growing numbers of sites and connections6,7,8. To address these challenges, we formulate a universal approach for mapping arbitrary networks to synthesized one-dimensional lattices with strictly local inhomogeneous couplings, where the dynamics at the excited site is exactly replicated. We present direct experimental observations in judiciously designed planar photonic structures, showcasing non-monotonic excitation decays associated with up to seven-dimensional hypercubic lattices, and demonstrate a novel sharp localization transition specific to four and higher dimensions. The unprecedented capability of experimentally exploring multi-dimensional dynamics and harnessing their unique features in one-dimensional lattices can find multiple applications in diverse physical systems, including photonic integrated circuits.