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Optical and Quantum Sensing and Precision Metrology

Non-Hermitian quantum sensing: fundamental limits and non-reciprocal advantages

Hoi-Kwan Lau, Aashish A. Clerk

Published Mar 4, 2021• 0 citations
Publisher

Abstract

Unconventional properties of non-Hermitian systems, such exceptional points, have recently been suggested as a resource for sensing. The impact of noise and utility in quantum regimes, however, remain highly debatable. In this talk, I will introduce a full theoretical framework to analyze the performance of a dispersive quantum non-Hermitian sensor; parts of our result have been included in our recent paper Lau & Clerk, Nat. Comm. 9, 4320 (2018). Our formalism fully accounts for noise effects in both classical and quantum regimes, and also fully treats a realistic and optimal measurement protocol based on coherent driving and homodyne detection. Focusing on two-mode devices, we derive fundamental bounds on the signal-to-noise (SNR) ratio for any such sensor. We use these to demonstrate that enhanced SNR ratio does not necessarily require any proximity to an exceptional point. Furthermore, we show that non-reciprocity is a powerful resource for sensing even when quantum noise exists.

DOI
10.1117/12.2586713

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Unconventional properties of non-Hermitian systems, such exceptional points, have recently been suggested as a resource for sensing. The impact of noise and utility in quantum regimes, however, remain highly debatable. In this talk, I will introduce a full theoretical framework to analyze the performance of a dispersive quantum non-Hermitian sensor; parts of our result have been included in our recent paper Lau & Clerk, Nat. Comm. 9, 4320 (2018). Our formalism fully accounts for noise effects in both classical and quantum regimes, and also fully treats a realistic and optimal measurement protocol based on coherent driving and homodyne detection. Focusing on two-mode devices, we derive fundamental bounds on the signal-to-noise (SNR) ratio for any such sensor. We use these to demonstrate that enhanced SNR ratio does not necessarily require any proximity to an exceptional point. Furthermore, we show that non-reciprocity is a powerful resource for sensing even when quantum noise exists.
Unconventional properties of non-Hermitian systems, such as the existence of exceptional points, have recently been suggested as a resource for sensing. The impact of noise and utility in quantum regimes however remains unclear. In this work, we analyze the parametric-sensing properties of linear coupled-mode systems that are described by effective non-Hermitian Hamiltonians. Our analysis fully accounts for noise effects in both classical and quantum regimes, and also fully treats a realistic and optimal measurement protocol based on coherent driving and homodyne detection. Focusing on two-mode devices, we derive fundamental bounds on the signal power and signal-to-noise ratio for any such sensor. We use these to demonstrate that enhanced signal power requires gain, but not necessarily any proximity to an exceptional point. Further, when noise is included, we show that nonreciprocity is a powerful resource for sensing: it allows one to exceed the fundamental bounds constraining any conventional, reciprocal sensor.
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.
Non-Hermitian dynamics has been widely studied to enhance the precision of quantum sensing; and non-reciprocity can be a powerful resource for non-Hermitian quantum sensing, as nonreciprocity allows to arbitrarily exceed the fundamental bound on the measurement rate of any reciprocal sensors. Here we establish fundamental limits on signal-to-noise ratio for reciprocal and nonreciprocal non-Hermitian quantum sensing. In particular, for two-mode linear systems with two coherent drives, an approximately attainable uniform bound on the best possible measurement rate per photon is derived for both reciprocal and nonreciprocal sensors. This bound is only related to the coupling coefficients and, in principle, can be made arbitrarily large. Our results thus demonstrate that a conventional reciprocal sensor with two drives can simulate any nonreciprocal sensor. This work also demonstrates a clear signature on how the excitation signals affect the signal-to-noise ratio in non-Hermitian quantum sensing.
Unconventional non-Hermitian properties have been harnessed to enhance quantum sensing. Non-reciprocity has been identified as a powerful resource for non-Hermitian sensing. However, it was demonstrated that with two coherent drives, reciprocal non-Hermitian sensors can attain the same limit as those of non-reciprocal sensors. In this paper we demonstrate the positive role played by the gain noise in making a reciprocal sensor to have an arbitrarily large sensitivity. To do this, we take the best possible measurement rate per photon as the figure of merit. It is found that for the single-drive case, the best possible measurement rate per photon of reciprocal and non-reciprocal sensors do not change in the ideal case where the gain and loss are ignored; For the two-drive case, the best performance of non-reciprocal sensors can still be made arbitrarily large no matter whether gain and loss are involved. The gain noise is however crucial for reciprocal sensors to have an arbitrarily large sensitivity. Usually the noise is regarded as a negative effect that can greatly degrade the performance of sensing, this work helps to better understand the positive role of gain in reciprocal sensing.
Non-Hermitian systems have been extensively studied in quantum metrology due to their unique properties, such as the skin effects, exceptional points, and the non-reciprocity. It has been demonstrated that although non-Hermitian systems may achieve ultra-high precision of quantum sensing, the measurement precision greatly depends on the position of the coherent drive in the regime of linear response. In this paper, we further investigate how the position of the coherent drive impacts the precision of non-Hermitian sensing in the regime beyond linear response. It is found that in contrast to the linear case, the best possible quantum Fisher information per photon of the sensor does not depend on the position of the coherent drive in the nonlinear perturbation regime.
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.