非线性奇异点传感中的定点分岔与路径信息界
Fixed-Point Bifurcations and Path-Information Bounds in Nonlinear Exceptional-Point Sensing
- School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
- International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（中国科学院大学亚太理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究证明非线性奇异点传感的奇异响应源于定点分岔，推导路径信息界表明信噪比增强有限，且在局部涨落区域可达到信息最优。
AI中文摘要：
非线性奇异点（NEP）被提出以规避限制线性奇异点传感器的噪声-响应抵消问题。在非线性奇异点处，稳态频率响应可以是奇异的，而哈密顿量Petermann因子保持有限，这表明了真正的信噪比（SNR）增强。然而，近期针对非线性涨落的模型特定分析得出了相互矛盾的结论。我们证明，任何奇异的稳态频率响应都需要非线性动力学的定点分岔。在局部涨落区域，响应率中的奇异性和长时间频率不确定性均由临界弛豫速率决定，导致信噪比中的精确抵消，并排除了任何发散性增强。此外，我们推导了一个路径信息界，该界适用于局部和非线性涨落区域，并对长时间信噪比增强设定了有限上限。值得注意的是，这一上限在局部涨落区域是可达到的，这意味着在此类参数设置下的频率读出是信息最优的。
英文摘要：
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.
