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arXiv:2407.14739 · Physical Review Applied

Quantum sensing with nonreciprocal couplings

Dong Xie, Chunling Xu

Published Dec 18, 2024• 7 citations
arXivHTMLPDF

Abstract

Nonreciprocity can not only generate quantum resources but can also shield noise and reverse interference from driving signals. We investigate the advantages of nonreciprocal coupling in sensing a driving signal. In general, we find that nonreciprocal coupling performs better than the corresponding reciprocal coupling. And we show that homodyne measurement is the optimal measurement. A single nonreciprocal coupling can increase measurement precision by up to 2 times. With the use of $N$ nonreciprocal couplings in parallel, the measurement precision can be increased by ${N}^{2}$ times compared with the corresponding reciprocal coupling. In a nonzero-temperature dissipative environment, we demonstrate that nonreciprocal quantum sensing has greater robustness regarding thermal noise than reciprocal quantum sensing.

DOI
10.1103/physrevapplied.22.064072

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Nonreciprocity can not only generate quantum resources but can also shield noise and reverse interference from driving signals. We investigate the advantages of nonreciprocal coupling in sensing a driving signal. In general, we find that nonreciprocal coupling performs better than the corresponding reciprocal coupling. And we show that homodyne measurement is the optimal measurement. A single nonreciprocal coupling can increase measurement precision by up to 2 times. With the use of NNN nonreciprocal couplings in parallel, the measurement precision can be increased by N2{N}^{2}N2 times compared with the corresponding reciprocal coupling. In a nonzero-temperature dissipative environment, we demonstrate that nonreciprocal quantum sensing has greater robustness regarding thermal noise than reciprocal quantum sensing.
Dispersive coupling is widely utilized for quantum information readout. Most prior studies have concentrated on reciprocal dispersive coupling. Here, we further construct nonreciprocal dispersive coupling and apply it to quantum sensing. For cavity photon number measurement, nonreciprocal dispersive coupling delivers higher precision than its reciprocal counterpart, and this advantage grows more pronounced with an increase in photon number. When directly measuring the single-photon driving strength, however, nonreciprocal dispersive coupling shows no superiority over reciprocal dispersive coupling. By converting the information of driving strength into cavity photon numbers via our proposed strategy, nonreciprocal dispersive coupling again outperforms reciprocal dispersive coupling in precision, with the advantage becoming increasingly significant at larger driving strength. This work presents a novel method to boost quantum sensing and enable the fabrication of ultra-precise quantum 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 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.
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.
Quantum nonreciprocity is a distinct and intriguing property in non-Hermitian systems, playing a crucial role in diverse fields, such as quantum information processing, quantum sensing as well as develping novel electronic devices. Particularly, in the range of linear response, quantum nonreciprocity has exhibited exponentially enhanced quantum sensing. However, its role remains unclear in the range beyond linear response. In this paper, we demonstrate that nonreciprocity itself may not help improve the sensitivity. To be specific, we find that when nonreciprocal systems, which are originally designed to exponentially improve the sensitivity of linear response signals, are employed to measure nonlinear response signals, the original precision index can no longer represent the actual measurement precision. We thus provide a crucial warning to employ nonreciprocity directly to measure nonlinear response signals. Our result implies that it may be necessary to carry out corresponding overall optimizations in order to fully exploit the advantages of nonreciprocity in sensing nonlinear response signals.
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.