Chiral state conversion near an exceptional point: speed-noise competition

TL;DR

This paper investigates how noise affects chiral state conversion near exceptional points in non-Hermitian systems, revealing a competition between speed and noise that influences chirality.

Contribution

It introduces a quantitative measure of chirality, analyzes its dependence on noise and speed, and establishes a scaling law for the transition between noisy and clean limits.

Findings

Chirality oscillations are highly sensitive to noise at slow speeds.

The competition between encircling speed and noise strength determines chirality.

A simple scaling law describes the boundary between noisy and clean regimes.

Abstract

One intriguing property of non-Hermitian systems is the breakdown of adiabatic theorem and chiral state conversion as the system dynamically encircles exceptional points. However, the subtle dependence of the chiral dynamics on the loop geometry, the starting point, the encircling speed and especially the noise has not been studied systematically. Here we propose a non-chirality degree $\chi_c$ to measure the chirality quantitatively and analyze it in dynamics without noise by exact solution and dynamics with noise by numerical integration. The exact dynamics starting from the broken phase show chirality oscillations, which are extremely sensitive to noise when the speed is small. The encircling speed and the noise strength are found to compete with each other in determining $\chi_c$, resulting in two distinguished limits, namely the noisy limit and the clean limit. The critical boundary between the two limits satisfies a simple scaling law, which could be explained in terms of first-order perturbation theory and the condition number of the transfer matrix. Our findings reveal the essential role played by noise in non-Hermitian dynamics and are relevant for both theoretical and experimental investigations.