Fluctuations and noise-limited sensing near the exceptional point of $\mathcal{PT}$-symmetric resonator systems

TL;DR

This paper investigates how mesoscopic fluctuations and noise influence the spectral, temporal, and sensing performance of $ ext{PT}$-symmetric resonator systems near the exceptional point, revealing challenges in maintaining stable operation.

Contribution

It provides a theoretical analysis of the impact of fluctuations and noise on $ ext{PT}$-symmetric resonators near the exceptional point, highlighting effects on spectral features and sensor stability.

Findings

Detuning modifies exceptional point conditions.

Spectral features are smeared by statistical averaging.

Temporal fluctuations cause quadratic power growth.

Abstract

We theoretically explore the role of mesoscopic fluctuations and noise on the spectral and temporal properties of systems of $\mathcal{PT}$-symmetric coupled gain-loss resonators operating near the exceptional point, where eigenvalues and eigenvectors coalesce. We show that the inevitable detuning in the frequencies of the uncoupled resonators leads to an unavoidable modification of the conditions for reaching the exceptional point, while, as this point is approached in ensembles of resonator pairs, statistical averaging significantly smears the spectral features. We also discuss how these fluctuations affect the sensitivity of sensors based on coupled $\mathcal{PT}$-symmetric resonators. Finally, we show that temporal fluctuations in the detuning and gain of these sensors lead to a quadratic growth of the optical power in time, thus implying that maintaining operation at the exceptional point over a long period can be rather challenging. Our theoretical analysis clarifies issues central to the realization of $\mathcal{PT}$-symmetric devices, and should facilitate future experimental work in the field.