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arXiv 1807.02157cond-mat.mes-hallphysics.optics
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$\mathcal{PT}$对称谐振器系统异常点附近的波动和噪声限制传感

Fluctuations and noise-limited sensing near the exceptional point of $\mathcal{PT}$-symmetric resonator systems

N. Asger Mortensen, P. A. D. Gonçalves, Mercedeh Khajavikhan, Demetrios N. Christodoulides, C. Tserkezis, C. Wolff

摘要:

我们从理论上探讨了介观波动和噪声的作用的频谱和时间特性的系统$\mathcal{PT}$对称耦合增益损耗谐振器附近的例外点,本征值和本征向量合并。我们表明,不可避免的失谐的非耦合谐振器的频率导致一个不可避免的修改的条件,达到例外的点,而这一点是接近合奏的谐振器对,统计平均显着涂抹的频谱特征。我们还讨论了这些波动如何影响传感器的灵敏度耦合$\mathcal{PT}$对称谐振器的基础上。最后,我们表明,这些传感器的失谐和增益的时间波动导致光功率在时间上的二次增长,从而意味着在很长一段时间内保持在异常点的操作可能是相当具有挑战性的。我们的理论分析阐明了实现$\mathcal{PT}$对称器件的核心问题,并应促进该领域未来的实验工作。

英文摘要:

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 the 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 also 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 a quadratic growth of the optical power in time, thus 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.

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