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arXiv:2303.16575 · Physical Review Research

Exponential sensitivity revival of noisy non-Hermitian quantum sensing with two-photon drives

Liying Bao, Bo Qi, Franco Nori, Daoyi Dong

Published May 28, 2024• 16 citations
arXivHTMLPDF

Abstract

Unique properties of multimode non-Hermitian lattice dynamics can be utilized to construct exponentially sensitive sensors. However, the impact of noise remains unclear, which may severely degrade their sensitivity. We analytically characterize and highlight the impact of loss and gain on the sensitivity revival and stability of non-Hermitian sensors. Defying the general belief that the superiority of quantum sensing will vanish in the presence of loss, we find that by proactively tuning the loss, the exponential sensitivity can be surprisingly regained when the sensing dynamics is stable. Furthermore, we prove that gain is crucial to fully revive the ideally exponential sensitivity and to ensure the stability of non-Hermitian sensing by making a balanced loss and gain. Our paper opens a way to significantly enhance the sensitivity by proactively tuning the loss and gain, which may promote future quantum sensing and quantum engineering. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023216

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Unique properties of multimode non-Hermitian lattice dynamics can be utilized to construct exponentially sensitive sensors. However, the impact of noise remains unclear, which may severely degrade their sensitivity. We analytically characterize and highlight the impact of loss and gain on the sensitivity revival and stability of non-Hermitian sensors. Defying the general belief that the superiority of quantum sensing will vanish in the presence of loss, we find that by proactively tuning the loss, the exponential sensitivity can be surprisingly regained when the sensing dynamics is stable. Furthermore, we prove that gain is crucial to fully revive the ideally exponential sensitivity and to ensure the stability of non-Hermitian sensing by making a balanced loss and gain. Our paper opens a way to significantly enhance the sensitivity by proactively tuning the loss and gain, which may promote future quantum sensing and quantum engineering. Published by the American Physical Society 2024
It has been shown that exponentially enhanced sensitivity can be obtained by utilizing quantum non-Hermitian properties, such as the skin effect. However, in previous works only the accompanied quantum noise in the input waveguide was considered, while the complex ambient gain and loss noises were not taken into account. In this work, we study the sensitivity of non-Hermitian quantum sensors under complex ambient noises. We find that the gain and loss structures play a crucial role in the sense that by finely adjusting the gain and loss, quantum sensors can recover its original exponential sensitivity. Our results provide an effective means to improve the performance of quantum sensors in real physical environments.
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 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.
Distinct non-Hermitian dynamics has demonstrated its advantages in improving measurement precision over traditional sensing protocols. Multimode non-Hermitian lattice dynamics can provide exponentially enhanced quantum sensing where the quantum Fisher information (QFI) per photon increases exponentially with the lattice size. However, it has also been shown that the quintessential non-Hermitian skin effect does not provide any true advantage. In this paper, we demonstrate the importance of optimizing the phase of the coherent drive and the position of the injection and detection in multimode non-Hermitian quantum sensing. The QFI per photon can be exponentially enhanced or exponentially reduced depending on the parameters of the drive and detection. Specifically, it is demonstrated that for large amplification, by choosing appropriate coherent drive parameters, the non-Hermitian skin effect can provide exponentially enhanced quantum sensing. Moreover, in the regime beyond linear response, the skin effect can also provide a clear advantage as compared to the local perturbation and the proposed protocol is robust in tuning the amplification factor.
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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.