Impact of noise on applications based on nonlinear exceptional points

Nonlinear exceptional points (NEPs), an emerging class of spectral singularities, are expected to address the challenges of noise divergence and complicated parameter tuning in linear EPs, attracting intense theoretical and experimental interest. Recently, however, it has been argued that the interplay between noise and nonlinearity degrades NEPs and thereby limits the performance of NEP-based applications, especially sensing. Here, we develop a rigorous framework to characterize this interplay and demonstrate the superior advantages of NEP. Taking NEP-based sensors---the most noise-affected case---as a representative example, we show that their signal-to-noise ratio (SNR), the core figure of merit, can be significantly enhanced at NEPs owing to a hidden nonlinear feedback mechanism. Our results advance the theoretical understanding of noise in nonlinear systems, resolve the ongoing debate on the SNR of NEP-based sensors, and take essential steps toward the practical realization of diverse NEP-related applications.