论文标题
线性谐波振荡器共振频率测量的热力学极限
Thermodynamic Limit for Linear Harmonic Oscillator Resonance Frequency Measurement
论文作者
论文摘要
机械谐振器中的热力学波动会导致其频率测量的不确定性，从根本上限制了基于频率的传感器的性能。最近，将纳米光学运动读数与微力和纳米机械谐振器相结合，可以使实用的芯片尺度传感器在高频带宽度测量中常规运行。但是，热力学频率测量不确定性或有效，实时频率估计器的精确和一般表达不清，尤其是对于快速和弱驱动的谐振器。在这里，我们得出并在数值上验证了CRAMER-RAO下限（CRLB）和经典线性谐波振荡频率的有效最大样本估计器，但受热力学波动。 For a fluctuating oscillator without external drive, the frequency Allan deviation calculated from simulated resonator motion data agrees with the derived CRLB $σ_f = {1 \over 2π}\sqrt{Γ\over 2τ}$ for averaging times $τ$ below, as well as above, the relaxation time $1\overΓ$. CRLB方法是一般的，可以扩展到驱动的谐振器，不可忽略的运动检测不精确以及连续线性量子测量的反击。
Thermodynamic fluctuations in mechanical resonators cause uncertainty in their frequency measurement, fundamentally limiting performance of frequency-based sensors. Recently, integrating nanophotonic motion readout with micro- and nano-mechanical resonators allowed practical chip-scale sensors to routinely operate near this limit in high-bandwidth measurements. However, the exact and general expressions for either thermodynamic frequency measurement uncertainty or efficient, real-time frequency estimators are not well established, particularly for fast and weakly-driven resonators. Here, we derive, and numerically validate, the Cramer-Rao lower bound (CRLB) and an efficient maximum-likelihood estimator for the frequency of a classical linear harmonic oscillator subject to thermodynamic fluctuations. For a fluctuating oscillator without external drive, the frequency Allan deviation calculated from simulated resonator motion data agrees with the derived CRLB $σ_f = {1 \over 2π}\sqrt{Γ\over 2τ}$ for averaging times $τ$ below, as well as above, the relaxation time $1\overΓ$. The CRLB approach is general and can be extended to driven resonators, non-negligible motion detection imprecision, as well as backaction from a continuous linear quantum measurement.
