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arXiv:2403.08218 · Physical Review Letters

Non-Hermitian Sensing in the Absence of Exceptional Points

Lei Xiao, Yaoming Chu, Quan Lin, Hai-Qing Lin, Wei Yi, Jianming Cai, Peng Xue

Published Oct 28, 2024• 44 citations
arXivHTMLPDF

Abstract

Open systems possess unique potentials in high-precision sensing, yet the majority of previous studies rely on the spectral singularities known as "exceptional points." Here, we theoretically propose and experimentally demonstrate universal non-Hermitian sensing in the absence of exceptional points. The scheme makes use of the intrinsic sensitivity of a non-Hermitian probe to weak external fields, which can be understood as the direct consequence of non-Hermiticity. We confirm the basic mechanism by simulating the sensor-field dynamics using photon interferometry, and, as a concrete example, demonstrate the enhanced sensing of signals encoded in the setting angle of a wave plate. While the sensitivity of the probe is ultimately limited by the measurement noise, we find the non-Hermitian sensor showing superior performance under background noises that cannot be suppressed through repetitive measurements. Our experiment opens the avenue of enhanced sensing without exceptional points, complementing existing efforts aimed at harnessing the unique features of open systems.

DOI
10.1103/physrevlett.133.180801

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Open systems possess unique potentials in high-precision sensing, yet the majority of previous studies rely on the spectral singularities known as "exceptional points." Here, we theoretically propose and experimentally demonstrate universal non-Hermitian sensing in the absence of exceptional points. The scheme makes use of the intrinsic sensitivity of a non-Hermitian probe to weak external fields, which can be understood as the direct consequence of non-Hermiticity. We confirm the basic mechanism by simulating the sensor-field dynamics using photon interferometry, and, as a concrete example, demonstrate the enhanced sensing of signals encoded in the setting angle of a wave plate. While the sensitivity of the probe is ultimately limited by the measurement noise, we find the non-Hermitian sensor showing superior performance under background noises that cannot be suppressed through repetitive measurements. Our experiment opens the avenue of enhanced sensing without exceptional points, complementing existing efforts aimed at harnessing the unique features of open systems.
High-precision sensors are of fundamental importance in modern society and technology. Although there are various schemes for the construction of sensors relying on different physical mechanisms, obtaining sensors with higher levels of sensitivity and stronger robustness has always been expected. In particular, non-Hermitian quantum sensors have recently attracted substantial attention due to their unique properties. So far, 2 types of non-Hermitian sensors based on exceptional points and topological zero modes have been realized. Here, high-order exceptional bound states with robust properties are constructed for the first time. Based on these states, we propose theoretically and demonstrate experimentally another new type of non-Hermitian quantum sensors. Such sensors not only are robust against disorders but also have unprecedented sensitivity. Their sensing performance can display the improvement of many orders of magnitude over the previous non-Hermitian sensors. Furthermore, we design and fabricate such sensors based on circuit networks. Taking weak magnetic field detection as an example, we also experimentally demonstrate their sensing capabilities. Our work opens up new avenues for the development of highly sensitive sensors, which have a wide range of applications in various fields.
Non-Hermitian systems have emerged as a powerful paradigm for ultrasensitive sensing, leveraging unique spectral and dynamical properties unmatched in Hermitian physics. While recent theoretical bounds suggest these protocols offer no metrological advantage over Hermitian ones in the ideal shot-noise-limited regime when rigorously accounting for the success probability of non-unitary evolution, their practical utility in realistic experimental conditions has not yet been systematically explored. In this work, we shift the focus toward practical laboratory performance and demonstrate that non-Hermitian sensing protocols can significantly outperform their Hermitian counterparts in the presence of pervasive classical technical noises. This performance gain mainly stems from a strongly enhanced susceptibility that amplifies the signal response, effectively overcoming the precision floor imposed by technical imperfections. By numerically evaluating the Fisher information under technical noise, we further substantiate the regimes where non-Hermitian platforms yield definitive practical gains. Our results reconcile the ongoing debate between fundamental limits and experimental observations, offering a concrete avenue for building high-precision, noise-resilient sensors.
Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation of parity-time symmetry, or capitalizing on the singular behavior of the dynamics. In this Letter, we focus on the possibility of achieving unbounded sensitivity when using the system to sense linear perturbations away from a singular point. By combining multiparameter estimation theory of Gaussian quantum systems with the one of singular-matrix perturbations, we introduce the necessary tools to study the ultimate limits on the precision attained by such singularity-tuned sensors. We identify under what conditions and at what rate can the resulting sensitivity indeed diverge, in order to show that nuisance parameters should be generally included in the analysis, as their presence may alter the scaling of the error with the estimated parameter.
Pushing the boundaries of measurement precision is central for sensing and metrology, pursued by nonclassical resources such as squeezing, as well as non-Hermitian degeneracies with distinct spectral response. Their convergence, however, remains challenging. We find extraordinary enhancement of sensitivity by unifying both effects in a general framework for quantum sensing in open systems. At the parametric oscillation threshold and an exceptional point, the sensing precision exhibits a unique quartic scaling with the perturbation strength. The result generalizes to multimode squeezed-state sensors with higher-order exceptional points catered to various quantum sensing platforms.
Abstract Parity-time (PT)-symmetric non-Hermitian systems exhibit a heightened sensitivity to external environmental changes, making them a popular choice in the field of quantum sensing. In this study, we designed a small tilt sensor based on the exceptional point (EP) of non-Hermitian systems. The measurement sensitivity of the sensor can be increased by a factor of 10000 times when compared with that of traditional sensors. However, in terms of the measurement precision of the EP sensor, there was no significant improvement because the EP sensor amplified the signal while amplifying the noise. Nonetheless, EP sensors retain clear advantages in specialized scenarios, such as detector saturation events, during which they surpass traditional sensors. Subsequently, we increased the measurement precision of the EP sensor by 2 n + 1 times by using high-order Hermite-Gaussian (HG) light, where n denotes the mode order of the signal light. Finally, we conclude this study with an analysis of the noise in EP sensors based on quantum error theory. Furthermore, we explore how EP sensors can strike a balance between high sensitivity and precision by incorporating a squeezed light field with elevated HG modes.
Exceptional-point (EP) sensing has attracted considerable interest because of its anomalous response scaling. However, recent studies have shown that the enhanced response near an EP is inevitably accompanied by amplified quantum noise, fundamentally limiting the achievable signalto-noise ratio (SNR). Here, we propose a fundamentally different route toward non-Hermitian quantum sensing based on symmetry-protected noise suppression rather than response amplification. We develop a fully quantum continuous-variable model that unifies parity-time (PT) and anti-paritytime(APT) symmetries within a single framework. Exploiting the incompatibility between these two symmetries, we uncover a non-Hermitian Dirac eigenspectrum and reveal a hidden symmetryprotected phase transition embedded in the Hamiltonian spectrum. Remarkably, this hidden phasetransition simultaneously constitutes a symmetry-protected vacuum-noise fixed point, where collective three-mode quadratures exhibit suppressed quantum fluctuations despite the absence of any anomalous spectral response. As a consequence, quantum sensing is enhanced through the suppression of excess quantum noise while maintaining a finite response sensitivity, establishing a sensing mechanism fundamentally different from conventional EP-based approaches. These results reveal an unexpected connection between hidden symmetry, quantum fluctuations, and non-Hermitian quantum metrology, and establish noise suppression as an alternative paradigm for non-Hermitian quantum sensing.