标题： 具有线性和二次位置耦合的光机械系统：动力学和最优估计 显示英文标题

标题： Optomechanical Systems with Linear and Quadratic Position Couplings: Dynamics and Optimal Estimation

摘要： 我们研究由单模光场与机械振子耦合组成的光机系统动力学，其中非线性相互作用包括振子位置的线性和二次项。 我们通过采用双声子相干态的形式理论，对该量子力学哈密顿量问题给出了完整的解析解。 量子估计理论被应用于光场的最终状态，重点是评估用于估计二次耦合强度的经典和量子费舍尔信息。 我们的估计方案考虑了标准和平衡外差光探测，假设初始光态为真空和单光子态的叠加。 我们表明，平衡外差检测可以达到量子费舍尔信息，从而达到估计二次耦合的终极精度界限。 此外，我们在一个实际实验背景下研究了热噪声对量子费舍尔信息的影响。 显示英文摘要

摘要： We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We present a full analytical solution to this quantum mechanical Hamiltonian problem by employing the formalism of two-phonon coherent states. Quantum estimation theory is applied to the resulting state of the optical field, with a focus on evaluating the classical and quantum Fisher information for estimating the strength of the quadratic coupling. Our estimation scheme considers both standard and balanced homodyne photodetection, assuming an initial optical state prepared as a superposition of vacuum and single-photon states. We show that balanced homodyne detection can saturate the quantum Fisher information, thus reaching the ultimate precision bound for estimating the quadratic coupling. Additionally, we investigate the effect of thermal noise on the quantum Fisher information in a realistic experimental context.