Exponential Sensitivity Revival and Robust Stability of Noisy non-Hermitian Quantum Sensing

Unique properties of multimode non-Hermitian (NH) lattice dynamics can be utilized to construct exponentially sensitive sensors. The impact of noise however remains unclear, which may greatly degrade the ability to detect small parameter changes. We analytically characterize and highlight the impact of the structure of loss and gain on the sensitivity and stability of NH quantum sensors. Counter-intuitively, we find that by only tuning the loss structure properly, the exponential sensitivity can be surprisingly regained when the sensing dynamics is stable. Furthermore, we prove that the gain is crucial to ensure the stability of the NH sensor by making a balanced loss and gain. For unbalanced noise, we demonstrate that there is a striking tradeoff between the enhancement of the sensitivity and the exponential decrement of the robust stability. This work demonstrates a clear signature about the impact of noise on the sensitivity and stability of NH quantum sensors, and has potential applications in quantum sensing and quantum engineering.