Noise-Induced Limits on Responsivity and SNR for Nonlinear Exceptional Point Sensing

Exceptional points (EPs) have been suggested for ultra-sensitive sensing because the eigenfrequency splitting grows as the nth-root of a perturbation, suggesting divergent responsivity. In ideal linear devices, however, this responsivity gain is reconciled by a matching divergence in the quantum shot-noise floor, so the net signal-to-noise ratio remains unchanged. Recent work has extended this argument to nonlinear devices, such as above-threshold lasers, predicting other divergences at an EP that is shifted by the interplay of noise and saturation effects. Here we analyze a system of two coupled saturable resonators and show analytically that a self-consistent treatment of fluctuation dynamics removes these divergences entirely. Islands of instability arise in the parameter space surrounding the EP due to the coupling of phase noise into the amplitude dynamics, dictating a maximum responsivity and maximum noise that can be experimentally observed. Stochastic Langevin simulations of the full nonlinear system corroborate our analytical results down to zero detuning.