# Extreme defect sensitivity from large synthetic dimensionality

## TL;DR

This paper introduces a method to simulate high-dimensional systems using static one-dimensional photonic lattices, revealing extreme defect sensitivity and new bound states, with potential applications in ultra-sensitive sensing and quantum technologies.

## Contribution

The authors present a novel approach to emulate up to 7D systems with 1D structures, enabling exploration of high-dimensional effects in photonics and beyond.

## Key findings

- Demonstrated non-monotonic excitation decay in 7D equivalent lattices
- Discovered a new bound state at the continuum edge in higher dimensions
- Observed extreme sensitivity to defect site detuning in 5D mapped systems

## Abstract

The geometric dimensionality of a physical system significantly impacts its fundamental characteristics. While experiments are fundamentally limited to the maximum of three spatial dimensions, there is a growing interest in harnessing additional synthetic dimensions. In our work, we introduce a new paradigm for the experimental realization of excitation dynamics associated with many-dimensional systems. Crucially, it relies solely on static one-dimensional equivalent structures with judiciously tailored parameters to faithfully reproduce the same optical spectrum and density of states of the high-dimensional system to be represented. In order to showcase the capabilities of our approach, we fabricate 1D photonic lattices that exhibit the characteristic non-monotonic excitation decays associated with quantum walks in up to 7D square lattices. Furthermore, we find that a new type of bound state at the edge of the continuum emerges in higher-than-three dimensions and gives rise to a sharp localisation transition at defect sites. In a series of experiments, we implement the mapped equivalent lattices of up to 5D systems and observe an extreme increase of sensitivity with respect to the detuning of the respective anchor sites. Our findings demonstrate the feasibility and applicative potential of harnessing high-dimensional effects in planar photonics for ultra-sensitive switching or sensing. Notably, our general approach is by no means limited to optics, and can readily be adapted to a variety of other physical contexts, including cold atoms and superconducting qubits with exclusively nearest-neighbour interactions, promising to drive significant advances in different fields including quantum simulations and information processing.