Fixed-Point Bifurcations and Path-Information Bounds in Nonlinear Exceptional-Point Sensing
Year: 2026
Type: preprint
Abstract: Nonlinear exceptional points (NEPs) were proposed to circumvent the noise--responsivity cancellation that limits linear exceptional-point sensors. At an NEP, the stationary frequency response can be singular while the Hamiltonian Petermann factor remains finite, suggesting a genuine signal-to-noise ratio (SNR) enhancement. Yet recent model-specific analyses of nonlinear fluctuations have reached conflicting conclusions. We prove that any singular stationary frequency response requires a fixed-point bifurcation of the nonlinear dynamics. In local fluctuation regimes, the singularities in responsivity and long-time frequency uncertainty are both set by the critical relaxation rate, leading to exact cancellation in the SNR and precluding any divergent enhancement. Furthermore, we derive a path-information bound that applies across both local and nonlinear fluctuation regimes and places a finite ceiling on the long-time SNR enhancement. Notably, this upper bound is attainable in the local fluctuation regime, implying that frequency readout under such parameter settings is information-optimal.
Source: arXiv (Cornell University)
Authors: Yu, Xue-Hao, Qiao, Cong-Feng
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G146487066, G3109392636
OpenAlex ID: W7215058567