We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity cannot only be further enhanced by injecting squeezed states of the cavity field, but also by modulating the light–matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nanogram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.

中文翻译：

---

量子光机械系统对时变引力场的最佳估计

我们研究了在非线性状态下使用理想的光机械系统来测量随时间变化的重力场所能实现的基本灵敏度。使用最新开发的方法来求解具有时变哈密顿量的非线性光学机械系统的动力学，我们计算了由于重力引起的机械元件线性位移的量子Fisher信息。我们证明，不仅可以通过注入腔场的压缩状态来进一步提高灵敏度，还可以通过调制光机械系统的光-质耦合来进一步提高灵敏度。我们专门将我们的结果应用于小振动质量的重力场的测量，从原理上我们表明，可以根据实验参数检测振荡的纳克质量的重力场，这些参数可能会在不久的将来获得。最后，我们确定了使用量子光机械传感器进行重力波检测所必需的实验参数范围。