AI 中文总结
研究利用有效捕获原子-腔模型，通过求解封闭系统载波动力学推导联合原子-腔态的位移框架量子费希尔信息，探讨其与引力加速度的关系，给出不同位置的检测方法及条件，表明腔损耗影响QFI，且载波模型QFI与未扩展模型一致。
AI 中文摘要
我们推导了一个有效的捕获原子-腔模型，其中恒定的引力加速度会改变振荡器平衡并改变局部驻波耦合，从而在杰恩斯·卡明斯交换频率中编码加速度。在原子和运动最初处于基态且腔场最初为相干态的情况下，我们精确求解了封闭系统的载波动力学，并推导了联合原子-腔态的位移框架量子费希尔信息（QFI）。该QFI与局部耦合斜率的平方成正比，随询问时间呈二次增长，并与平均光子数呈线性比例。在节点处，相位参考拉姆齐检测给出轴向加速度的符号敏感估计，并局部饱和联合QFI。在远离节点处，当腔态携带的QFI比原子态更多时，光子计数和相位优化零差检测可提供腔读出。在所研究的离节点工作点，林德布拉德模拟表明腔损耗产生有限时间的QFI最优值。兰姆-迪克条件和边带抑制条件控制载波近似。在封闭系统基准中，载波模型的QFI与在去除运动后从未扩展模型获得的原子-腔QFI一致。
英文摘要
We derive an effective trapped atom--cavity model in which a constant gravitational acceleration shifts the oscillator equilibrium and changes the local standing-wave coupling, thereby encoding the acceleration in the Jaynes Cummings exchange frequencies. With the atom and motion initially in their ground states and the cavity field initially coherent, we solve the closed-system carrier dynamics exactly and derive the displaced-frame quantum Fisher information (QFI) of the joint atom-cavity state. This QFI is proportional to the square of the local coupling slope, grows quadratically with interrogation time, and scales linearly with mean photon number. At the node, phase-referenced Ramsey detection gives a sign-sensitive estimate of axial acceleration and locally saturates the joint QFI. Away from the node, photon counting and phase-optimized homodyne detection provide cavity readouts when the cavity state carries more QFI than the atomic state. At the off-node operating point studied, Lindblad simulations show that cavity loss produces a finite-time QFI optimum. Lamb Dicke and sideband-suppression conditions control the carrier approximation. In the closed-system benchmark, the carrier-model QFI agrees with the atom-cavity QFI obtained from the unexpanded model after tracing out motion.
Comments26 pages 8 figures
