Backaction-evading (BAE) measurements of a mechanical resonator, by continuously monitoring a single quadrature of motion, can achieve precision below the zero-point uncertainty. When this happens, the measurement leaves the resonator in a quantum squeezed state. The squeezed state so generated is however conditional on the measurement outcomes, while for most applications it is desirable to have a deterministic, i.e., unconditional, squeezed state with the desired properties. In this work we apply feedback control to achieve deterministic manipulation of mechanical squeezing in an optomechanical system subject to a continuous BAE measurement. We study in details two strategies, direct (Markovian) and state-based (Bayesian) feedback. We show that both are capable to achieve optimal performances, i.e., a vanishing noise added by the feedback loop. Moreover, even when the feedback is restricted to be a time-varying mechanical force (experimentally friendly scenario) and an imperfect BAE regime is considered, the ensuing nonoptimal feedback may still obtain significant amount of squeezing. In particular, we show that Bayesian feedback control is nearly optimal for a wide range of sideband resolution. Our analysis is of direct relevance for ultrasensitive measurements and quantum state engineering in state-of-the-art optomechanical devices.

中文翻译：

---

通过回避回避测量和非最佳反馈控制进行无条件机械挤压

通过连续监视单个正交运动，可以对机械谐振器进行反作用规避（BAE）测量，从而可以在零点不确定度以下实现精度。发生这种情况时，测量结果会使谐振器处于量子压缩状态。然而，如此产生的挤压状态取决于测量结果，而对于大多数应用，期望具有确定的，即无条件的，具有期望特性的挤压状态。在这项工作中，我们应用反馈控制来实现对光机械系统进行连续BAE测量的机械挤压的确定性操作。我们详细研究了两种策略，直接（马尔可夫）和基于状态（贝叶斯）的反馈。我们表明，两者都能够实现最佳性能，即反馈环路增加的消失噪声。此外，即使当反馈被限制为随时间变化的机械力（实验上很友好的情况）并且考虑到不完善的BAE机制时，随后出现的非最佳反馈仍可能会导致大量的压缩。特别是，我们表明贝叶斯反馈控制对于宽边带分辨率范围几乎是最佳的。我们的分析与最先进的光机械设备中的超灵敏测量和量子态工程直接相关。