Fixed-Point Bifurcations and Path-Information Bounds in Nonlinear Exceptional-Point Sensing

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.

Quantum Physics (quant-ph); Optics (physics.optics)

arXiv:2609.39046 [quant-ph]

(or arXiv:2609.39046v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.39046 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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