Reconsidering resonator sensing Changes in the frequency of a nanoscale mechanical resonator can be used for many sensing applications, provided that there is an adequate signal-to-noise ratio. Normally, this ratio is improved by creating resonators with higher quality factors that “ring” for longer times. Taking a cue from the approaches used in atomic force microscopy, Roy et al. show that if the thermomechanical noise of the resonator is well defined, the signal-to-noise ratio of the frequency shift can improve by lowering the quality factor. They used this approach to demonstrate temperature sensing with a double-clamped silicon beam resonator, which performed better at ambient pressures than in a vacuum. Science, this issue p. eaar5220 Resonators with well-defined thermomechanical noise can perform better at ambient pressure than in vacuum. INTRODUCTION Nano-optomechanical systems (NOMS) are very small resonating mechanical devices that have extraordinary sensitivity. The coupling of mechanical motion to an optical cavity allows the motion to be tracked with femtometer precision. When using NOMS (or their electrical cousin, nanoelectromechanical systems) as a stable frequency reference, tiny force and mass changes can be distinguished by small frequency shifts. This is useful in atomic force microscopy and ultrasensitive mass measurement. For example, improvements in mass sensitivity have enabled the resolution of single molecules and have launched a prospective new paradigm of mechanical mass spectrometry. Any method to improve stability improves the performance of these sensors. If stability could remain the same or improve with more damping, NOMS ultrasensitivity could be deployed in a damping medium, like air or liquid, greatly enhancing their utility for use as biosensors or gas sensors or in the environment. Better stability could also benefit oscillator clock electronics, which could ultimately improve technologies such as GPS. RATIONALE The quality factor (Q) is the inverse of the damping and indicates how sharp the resonance is in frequency. Q has been used as a proxy metric for frequency stability. However, Q only provides half the contribution; the other half comes from how large the resonance signal is compared to noise [the signal-to-noise ratio (SNR)]. This relationship is known as Robins’ model. Although traditionally Q and SNR have been assumed to be correlated, we noted that when the resonance conditions are limited only by intrinsic factors, the SNR should be inversely proportional to Q. In this case, stability should be independent of Q, and stable performance should be maintained in a variety of damping conditions. RESULTS We measured intrinsic resonator stability in NOMS while decreasing Q by increasing the air pressure around the device. We found that SNR behaved inversely to Q as hypothesized; however, stability unexpectedly improved with decreasing Q. This improved performance with damping is diametrically opposed to conventional expectations that had been established for decades. We revisited Robins’ model to find that it was based on a high-Q approximation. Rederiving the model without approximation gave rise to a new flatband regime for large damping (low Q). In this new regime, stability tracked to SNR only and, correspondingly, improved with damping, explaining the measured data. We confirmed the improved performance at higher damping by monitoring temperature fluctuations at different pressures and found that the best stability occurred at highest SNR, consistent with the new model. Finally, there is a noise source called dephasing that is known to prevent mechanical resonators from reaching their stability limits. We confirmed that this extra noise source correlated with Q and therefore was mitigated at large damping and removed completely at atmospheric pressure. CONCLUSION Our measurements confirm that Q and SNR behave inversely for intrinsically limited resonators, refuting long-standing assumptions about Q as a stability proxy. More notably, we found stability improved with damping. A low-Q approach was further shown to elegantly solve a vexing stability limitation caused by dephasing. We rederived Robins’ model to find a new flatband regime in which stability is linked only to SNR and found the new model to be consistent with the measured data. The flatband model displayed intriguing properties (in addition to stability behaving inversely to Q), including moderation of the trade-off between low noise and bandwidth and a route to frequency-scaling enhancement. The results offer a new paradigm for thinking about stability in mechanical resonators and suggest new pathways to improve stability in resonant sensors and crystal clock oscillators. Higher SNR leads to better stability. A mechanical resonator operating near intrinsic limits (e.g., limited only by thermomechanical noise and driven to the end of its linear regime) has a higher SNR in a low-Q state. SNR correlates to stability; frequency fluctuations are higher in the high-Q case. The surprising result is that low-Q devices can make better sensors and oscillators. (Inset) Cartoon of a NOMS chip with a waveguide bus (top), racetrack optical resonator (middle), and mechanical resonant doubly clamped beam (bottom). Beam motion is monitored with high precision through evanescent field interaction with and amplification by the optical cavity. Mechanical resonances are used in a wide variety of devices, from smartphone accelerometers to computer clocks and from wireless filters to atomic force microscopes. Frequency stability, a critical performance metric, is generally assumed to be tantamount to resonance quality factor (the inverse of the linewidth and of the damping). We show that the frequency stability of resonant nanomechanical sensors can be improved by lowering the quality factor. At high bandwidths, quality-factor reduction is completely mitigated by increases in signal-to-noise ratio. At low bandwidths, notably, increased damping leads to better stability and sensor resolution, with improvement proportional to damping. We confirm the findings by demonstrating temperature resolution of 60 microkelvin at 300-hertz bandwidth. These results open the door to high-performance ultrasensitive resonators in gaseous or liquid environments, single-cell nanocalorimetry, nanoscale gas chromatography, atmospheric-pressure nanoscale mass spectrometry, and new approaches in crystal oscillator stability.

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通过更大的阻尼提高机械传感器性能

重新考虑谐振器传感 纳米级机械谐振器频率的变化可用于许多传感应用，前提是有足够的信噪比。通常，通过创建具有更高品质因数且“振铃”时间更长的谐振器来改善该比率。从原子力显微镜中使用的方法中获取线索，Roy 等人。表明如果谐振器的热机械噪声定义明确，则可以通过降低品质因数来改善频移的信噪比。他们使用这种方法来演示双钳位硅梁谐振器的温度传感，该谐振器在环境压力下比在真空中表现更好。科学，这个问题 p。eaar5220 具有明确热机械噪声的谐振器在环境压力下的性能比在真空中更好。介绍 纳米光机械系统 (NOMS) 是非常小的共振机械设备，具有非凡的灵敏度。机械运动与光学腔的耦合允许以飞米精度跟踪运动。当使用 NOMS（或它们的电表兄弟，纳米机电系统）作为稳定的频率参考时，微小的力和质量变化可以通过小的频率偏移来区分。这在原子力显微镜和超灵敏质量测量中很有用。例如，质量灵敏度的提高使单个分子的分辨率成为可能，并启动了机械质谱的前瞻性新范式。任何提高稳定性的方法都可以提高这些传感器的性能。如果稳定性可以保持不变或通过更大的阻尼改善，NOMS 超灵敏度可以部署在阻尼介质中，如空气或液体，大大增强了它们用作生物传感器或气体传感器或在环境中的效用。更好的稳定性也有利于振荡器时钟电子学，这最终可以改进 GPS 等技术。基本原理 品质因数 (Q) 是阻尼的倒数，表示共振频率的尖锐程度。Q 已被用作频率稳定性的代理指标。但是，Q 只提供了一半的贡献；另一半来自共振信号与噪声相比的大小 [信噪比 (SNR)]。这种关系被称为罗宾斯模型。尽管传统上假设 Q 和 SNR 是相关的，但我们注意到，当谐振条件仅受内在因素限制时，SNR 应该与 Q 成反比。在这种情况下，稳定性应该与 Q 无关，并且在各种阻尼条件下都应该保持稳定的性能。结果 我们测量了 NOMS 中固有谐振器的稳定性，同时通过增加设备周围的气压来降低 Q。我们发现 SNR 的表现与假设的 Q 成反比；然而，随着 Q 值的降低，稳定性出乎意料地提高。这种改进的阻尼性能与几十年来建立的传统预期截然相反。我们重新审视了 Robins 的模型，发现它基于高 Q 近似值。在没有近似的情况下重新推导模型产生了大阻尼（低 Q）的新平带机制。在这个新机制中，稳定性仅跟踪 SNR，并且相应地随着阻尼而改善，解释测量数据。我们通过监测不同压力下的温度波动证实了更高阻尼下的性能改进，并发现最佳稳定性出现在最高 SNR 时，与新模型一致。最后，有一种称为移相的噪声源，众所周知，它会阻止机械谐振器达到其稳定性极限。我们确认这个额外的噪声源与 Q 相关，因此在大阻尼下得到缓解，并在大气压下完全消除。结论我们的测量证实 Q 和 SNR 对于本质上有限的谐振器表现相反，驳斥了关于 Q 作为稳定性代理的长期假设。更值得注意的是，我们发现阻尼可以提高稳定性。进一步证明了低 Q 方法可以优雅地解决由移相引起的令人烦恼的稳定性限制。我们重新推导了 Robins 的模型，以找到一种新的平带机制，其中稳定性仅与 SNR 相关，并发现新模型与测量数据一致。平带模型显示出有趣的特性（除了与 Q 成反比的稳定性之外），包括调节低噪声和带宽之间的权衡以及频率缩放增强的途径。结果为思考机械谐振器的稳定性提供了新的范例，并提出了提高谐振传感器和晶体时钟振荡器稳定性的新途径。更高的 SNR 导致更好的稳定性。接近固有极限运行的机械谐振器（例如，仅受热机械噪声限制并被驱动到其线性状态的末端）在低 Q 状态下具有更高的 SNR。SNR 与稳定性相关；在高 Q 情况下，频率波动更大。令人惊讶的结果是低 Q 值设备可以制造更好的传感器和振荡器。（插图）带有波导总线（顶部）、跑道光谐振器（中间）和机械谐振双钳位光束（底部）的 NOMS 芯片的卡通图。通过与光学腔的消逝场相互作用和放大，高精度地监测光束运动。机械共振用于各种各样的设备，从智能手机加速度计到计算机时钟，从无线滤波器到原子力显微镜。频率稳定性是一个关键的性能指标，通常被认为等同于谐振品质因数（线宽和阻尼的倒数）。我们表明，可以通过降低品质因数来提高谐振纳米机械传感器的频率稳定性。在高带宽下，信噪比的增加完全缓解了品质因数的降低。特别是在低带宽下，增加的阻尼会导致更好的稳定性和传感器分辨率，改进与阻尼成正比。我们通过展示 300 赫兹带宽下 60 微开尔文的温度分辨率来证实这些发现。这些结果为气体或液体环境中的高性能超灵敏谐振器、单细胞纳米量热法、纳米级气相色谱法、大气压纳米级质谱法和晶体振荡器稳定性的新方法打开了大门。信噪比的增加完全缓解了品质因数的降低。特别是在低带宽下，增加的阻尼会导致更好的稳定性和传感器分辨率，改进与阻尼成正比。我们通过展示 300 赫兹带宽下 60 微开尔文的温度分辨率来证实这些发现。这些结果为气体或液体环境中的高性能超灵敏谐振器、单细胞纳米量热法、纳米级气相色谱法、大气压纳米级质谱法和晶体振荡器稳定性的新方法打开了大门。信噪比的增加完全缓解了品质因数的降低。特别是在低带宽下，增加的阻尼会导致更好的稳定性和传感器分辨率，改进与阻尼成正比。我们通过展示 300 赫兹带宽下 60 微开尔文的温度分辨率来证实这些发现。这些结果为气体或液体环境中的高性能超灵敏谐振器、单细胞纳米量热法、纳米级气相色谱法、大气压纳米级质谱法和晶体振荡器稳定性的新方法打开了大门。