Fluctuations and noise-limited sensing near the exceptional point of parity-time-symmetric resonator systems

Exceptional points of parity-time (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 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 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 PT-symmetric devices, and should facilitate future experimental work in the field.