# Sensitivity Evaluation for Global Perturbations in Non‐Hermitian Skin‐Effect Sensors

## TL;DR

This paper explores how non-Hermitian sensors can detect global noise and disorder, showing that sensitivity increases exponentially with system size, enabling ultrasensitive sensing.

## Contribution

The study introduces a new method using maximum transient growth to detect global perturbations in non-Hermitian sensors.

## Key findings

- Sensitivity to global static and dynamic disorder scales exponentially with lattice size.
- Maximum transient growth, not spectral shifts, drives the observed exponential sensitivity.
- Non-Hermitian systems show potential for ultrasensitive detection of distributed fluctuations.

## Abstract

Non‐Hermiticity has introduced new physical mechanisms into sensing, with approaches based on exceptional points and non‐Hermitian skin effects demonstrating potential sensitivity enhancements over conventional sensing technologies. By monitoring the frequency shifts of specific eigenmodes, previous studies on non‐Hermitian sensors have revealed extraordinary sensitivity to local perturbations. In contrast, the influence of global perturbations such as noise and disorder, which generally involve complex spectra and may even suppress these eigenmodes, seems largely incompatible with the current non‐Hermitian sensing framework and has received far less attention. Here, motivated by recent theoretical advances on pseudospectra theory, we investigate the possibility of employing maximum transient growth to probe the level of global perturbations in non‐Hermitian skin‐effect sensors. Using discrete‐time light walks in synthetic photonic lattices, we experimentally evaluate the performance of a non‐Hermitian photonic lattice under static global phase noise. Remarkably, we demonstrate that the sensitivity grows exponentially with lattice size, manifesting in the maximum transient growth rather than the spectral shifts of previous non‐Hermitian skin‐effect sensors. Furthermore, numerical simulations reveal that this exponential sensitivity is preserved under dynamical perturbations. Our results highlight the limits as well as the potential of non‐Hermitian systems to tackle a wide range of sensing requirements for next‐generation ultrasensitive sensors.

Non‐Hermitian sensing against local and global noise. Conventional non‐Hermitian sensors focus on sensitivity against a static local boundary defect. Our work extends that framework to detect global perturbations. Using synthetic photonic lattices, we experimentally verify that sensitivity to global static and dynamic disorder scales exponentially with system size, unlocking the potential for ultrasensitive detection of distributed fluctuations or noise.