Impact of noise on nonlinear-exceptional-point-based sensors

Abstract: Nonlinear exceptional points (NEPs), a new type of spectral singularity in nonlinear non-Hermitian systems, are expected to address the noise divergence issue encountered at linear exceptional points and are therefore under the scrutiny of theoretical and experimental investigations. However, concerns have been raised that NEPs may hinder improvements in the signal-to-noise ratio (SNR) of sensors, and there is currently no rigorous theoretical framework to characterize noise effects in NEPs, particularly when accounting for the inherent nonlinear feedback. Here, we develop a new theoretical framework to address the impact of noise on NEP-based sensors, effectively resolving these concerns. The interplay between noise and nonlinearity keeps the average frequency virtually unchanged. In addition, a hidden feedback mechanism limits the increase in detectable uncertainty, together enabling a substantial SNR enhancement at NEPs. Our results resolve the ongoing debate over the SNR of NEPs and lay the groundwork for NEP-based sensor technologies.