Abstract
Non-Hermitian systems with gain and loss feature exceptional points (EPs) where eigenmodes and eigenfrequencies coalesce, offering ultrasensitive perturbation detection for sensing and topological wave control. Linear EPs provide high sensitivity via square-root frequency responses (Dw a Öϵ), but suffer from incomplete eigenbases and noise amplification. Nonlinear EPs (NEPs), as shown with onsite nonlinearity in coupled resonators [Bai et al., Phys. Rev. Lett. 132, 073802 (2024)], exhibit a third-order root law (Dw a ∛ϵ)) and amplify sensitivity by maintaining a complete eigenbasis, achieving a finite Petermann factor for enhanced signal-to-noise ratios. Recent work demonstrates nonlinearity-driven reversal of the non-Hermitian skin effect in resonator chains [Wu et al., arXiv:2410.16537 (2025)]. We explore NEPs in two-site systems with coupling nonlinearity, where amplitude-dependent nonreciprocal coupling induces frequency response and Petermann factor deviating from onsite nonlinearity, possibly opening new avenues for applications.
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