We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the signal-to-noise ratio to quantify the sensitivity of linear spectral measurements. Then we consider stationary force sensing and study the necessary conditions to minimize the added force noise. We find that imprecision noise and back-action noise can be arbitrarily suppressed by manipulating the amplitudes of the input coherent fields; however, the force noise power spectral density cannot be reduced below the level of thermal fluctuations. Therefore, we consider a nonstationary protocol that involves nonthermal dissipative state preparation followed by a finite time measurement, which allows one to perform measurements with a signal-to-noise ratio much greater than the maximum possible in a stationary measurement scenario. We analyze two different measurement schemes in the nonstationary transient regime: a back-action-evading measurement, which implies modifying the drive asymmetry configuration upon arrival of the force, and a nonstationary measurement that leaves the drive asymmetry configuration unchanged. Conditions for optimal force noise sensitivity are determined, and the corresponding force noise power spectral densities are calculated.

中文翻译：

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耗散机械量子压缩下的非平稳力传感

我们研究经典力的静态和非静态测量，该经典力在双音驱动下驱动耦合到电磁腔的机械振荡器。为此，我们开发了一种基于信噪比的理论框架来量化线性光谱测量的灵敏度。然后，我们考虑静止力感应并研究必要的条件，以最大程度地减小附加的力噪声。我们发现通过控制输入相干场的幅度可以任意地抑制不精确噪声和后向噪声。但是，力噪声功率谱密度不能降低到低于热波动的水平。因此，我们考虑了一个涉及非热耗散状态准备和有限时间测量的非平稳协议，它允许人们执行比信噪比大得多的测量，而信噪比要比固定测量情况下的最大值大。我们分析了非平稳瞬态情况下的两种不同的测量方案：回避作用的测量，这意味着在力到达后修改驱动器的不对称配置；以及一个使驱动器的不对称配置保持不变的非平稳的测量。确定最佳力噪声灵敏度的条件，并计算相应的力噪声功率谱密度。这意味着在力到达时修改驱动器不对称配置，以及使驱动器不对称配置保持不变的非平稳测量。确定最佳力噪声灵敏度的条件，并计算相应的力噪声功率谱密度。这意味着在力到达时修改驱动器不对称配置，以及使驱动器不对称配置保持不变的非平稳测量。确定最佳力噪声灵敏度的条件，并计算相应的力噪声功率谱密度。