Exceptional points of parity-time ($\mathcal{PT}$) symmetric systems hold an intriguing potential for highly sensitive sensors. Here, we theoretically explore the role of mesoscopic fluctuations and noise on the spectral and temporal properties of systems of $\mathcal{PT}$-symmetric-coupled gain–loss resonators operating near the exceptional point, where eigenvalues and eigenvectors coalesce. We show that experimentally inevitable detuning in the frequencies of the uncoupled resonators leads to an unavoidable modification of the conditions for reaching the exceptional point, while, as this point is approached in ensembles of resonator pairs, statistical averaging significantly smears the spectral features. We discuss how these fluctuations affect the sensitivity of sensors based on coupled $\mathcal{PT}$-symmetric resonators. Finally, we show that temporal fluctuations in the detuning and gain of these sensors lead to at least a quadratic growth of the optical power in time, implying that maintaining operation at the exceptional point over a long period can be rather challenging. Our theoretical analysis clarifies issues central to the realization of $\mathcal{PT}$-symmetric devices, and should facilitate future experimental work in the field.

中文翻译：

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奇偶时间对称谐振器系统异常点附近的波动和噪声受限感测

奇偶时间（$\mathcal{PT}$）对称系统对于高度灵敏的传感器具有诱人的潜力。在这里，我们从理论上探讨介观涨落和噪声对系统的光谱和时间特性的作用。$\mathcal{PT}$对称耦合增益损耗谐振器在异常点附近工作，特征值和特征向量在此处合并。我们表明，在实验中，未耦合谐振器频率的不可避免的失谐会导致达到例外点的条件的不可避免的修改，而随着这一点在谐振器对的集合中逐渐接近，统计平均会明显地涂污频谱特征。我们讨论了这些波动如何影响基于耦合的传感器的灵敏度$\mathcal{PT}$对称谐振器。最后，我们表明，这些传感器失谐和增益的时间波动至少会导致光功率在时间上呈二次方增长，这意味着长期将操作保持在异常点上可能会颇具挑战性。我们的理论分析澄清了实现目标的核心问题$\mathcal{PT}$对称装置，并应促进该领域未来的实验工作。