发表机构
School of Information Science and Engineering, Hunan Institute of Engineering; Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, XJ-Laboratory and Department of Physics, Hunan Normal University; Hunan Provincial Key Laboratory of Intelligent Sensors and Advanced Sensor Materials, and Department of Physics, Hunan University of Science and Technology; College of Physics and Electronic Engineering, Hengyang Normal University（湖南工程学院信息科学与工程学院; 湖南师范大学物理与电子科学学院; 湖南科技大学物理与电子科学学院; 衡阳师范学院物理与电子工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究确定了线性化腔光力学系统中估计单光子耦合的最优初始态，通过方差最大化与拉格朗日对偶获得闭式解，并证明NOON态饱和海森堡界，扩展至蓝边带、损耗及实验精度分析。
AI 中文摘要
我们找到了线性化腔光力学系统用于估计单光子耦合的量子Fisher信息的最优初始态。在红失谐（分束器）区域，相互作用在两个模式之间交换激发，对于纯输入，Fisher信息是激发交换算子方差的四倍，从而将优化简化为具有闭式解的方差最大化。当机械模式处于Fock态时，探针是简并的：任何满足光子数约束的态都是最优的，且具有许多声子的Fock参考态线性地增强每光子灵敏度。对于任意固定的机械参考态，最优态变为相位匹配的压缩真空态，这是通过拉格朗日对偶论证获得的该相干性的精确界得到的。在固定总激发数下联合优化两个模式时，量子Fisher信息满足能量二次方的海森堡界，该界由生成器的两个极值本征态的等权叠加饱和，等价于经过平衡分束器后的双模NOON态；平衡乘积Fock态仅达到线性增强。在截断Fock空间中的精确对角化证实了所有结果，熟悉的单光子输入是最简单的饱和情形。我们推导了三个扩展：蓝边带具有无界的双模压缩谱，因此纠缠最优变得不可能，平衡乘积Fock态在确定能量下精确最优；在腔损耗下，信息积累在腔寿命时间尺度上变为线性，更新最优持续时间约为两个半寿命；对于最先进的量子相干耦合实验，每小时相对精度介于百万分之一到百万分之十之间，数态和热态参考最为稳健。
英文摘要
We find the optimal initial states of a linearized cavity-optomechanical system for estimating the single-photon coupling by quantum Fisher information. In the red-detuned (beam-splitter) regime the interaction exchanges excitations between the two modes, and for pure inputs the Fisher information is four times the variance of the excitation-exchange operator, reducing the optimization to variance maximization with a closed-form solution. With the mechanical mode in a Fock state the probe is degenerate: any state saturating the photon-number constraint is optimal, and a Fock reference with many phonons enhances the per-photon sensitivity linearly. For an arbitrary fixed mechanical reference it becomes a phase-matched squeezed vacuum, from an exact bound on that coherence obtained by a Lagrange-dual argument. Jointly optimizing both modes at fixed total excitation number, the quantum Fisher information obeys a Heisenberg bound quadratic in the energy, saturated by equal superpositions of the two extremal eigenstates of the generator, equivalently a two-mode NOON state after a balanced beam splitter; balanced product Fock states reach only a linear enhancement. Exact diagonalization in truncated Fock spaces confirms all the results, the familiar single-photon input being the simplest saturating case. Three extensions are worked out: the blue sideband has an unbounded two-mode-squeezing spectrum, so the entangled optimum becomes impossible and the balanced product Fock state is exactly optimal at definite energy; under cavity loss the information accumulation turns linear on the cavity-lifetime timescale, at a renewal-optimal duration of about two and a half lifetimes; and for a state-of-the-art quantum-coherent coupling experiment the per-hour relative precision lies between one part in a million and ten parts in a million, number and thermal references being the most robust.
