Quantum Noise Theory of Exceptional Point Sensors

TL;DR

This paper develops a quantum noise theory for exceptional point sensors, analyzing how signal and noise are amplified at EPs, and demonstrates a scheme to optimize sensitivity using heterodyne detection.

Contribution

It introduces a systematic quantum noise framework for EP sensors and constructs a heterodyne detection scheme to achieve optimal sensitivity scaling.

Findings

EPs can amplify both signal and noise, affecting sensor performance.

Quantum Fisher information sets a lower bound on sensitivity.

Heterodyne detection achieves the ultimate sensitivity scaling.

Abstract

Distinct from closed quantum systems, non-Hermitian system can have exceptional points (EPs) where both eigenvalues and eigenvectors coalesce. Recently, it has been proposed and demonstrated that EPs can enhance the performance of sensors in terms of amplification of detected signal. Meanwhile, the noise might also be amplified at EPs and it is not obvious whether exceptional points will still improve the performance of sensors when both signal and noise are amplified. We develop quantum noise theory to systematically calculate the signal and noise associated with the EP sensors. We then compute quantum Fisher information to extract a lower bound of the sensitivity of EP sensors. Finally, we explicitly construct an EP sensing scheme based on heterodyne detection to achieve the same scaling of the ultimate sensitivity with enhanced performance. Our results can be generalized to higher order EPs for any bosonic non-Hermitian system with linear interactions.