发表机构
Leibniz Universität Hannover; University of Innsbruck; Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（汉诺威莱布尼茨大学; 因斯布鲁克大学; 奥地利科学院量子光学与量子信息研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出自旋网格态（SGSs）作为原子钟在自发辐射限制下的近最优量子探针，通过两次单轴扭转生成，并设计顺序读出策略，实现接近全局最优的相位和频率计量精度。
AI 中文摘要
纠缠可以增强相位估计和原子钟频率估计的精度，但在现实噪声过程下识别有用状态和测量方法仍是一个核心挑战。在此，我们研究受自发辐射影响的原子系综的量子计量，自发辐射通过限制有用的 interrogation 时间而限制了频率估计。我们确定自旋网格态（SGSs）为在系综规模超过51的交叉点之后的相关近最优探针，此时类GHZ态不再是最优的。SGSs在布洛赫球上显示周期性网格，并可通过两次由集体旋转分隔的单轴扭转（OAT）操作生成。通过优化置换对称态上的量子Fisher信息，我们发现SGSs在中等和大规模系综中表现接近全局最优探针，后者被证明是自旋GKP态。我们进一步提出一种顺序读出策略，该策略几乎饱和相应的量子Fisher信息。该策略使用OAT回波将自发辐射事件映射到集体旋转上，使相应的跳跃扇区可区分，并允许测量基根据衰变事件数量进行条件设置。总之，这些结果表明SGSs为自发辐射限制的原子系综中的量子增强相位和频率计量提供了一条实用途径。
英文摘要
Entanglement can enhance precision in phase estimation and in frequency estimation with atomic clocks, but it remains a central challenge to identify useful states and measurements under realistic noise processes. Here, we study quantum metrology with an ensemble of atoms subject to spontaneous emission, which limits frequency estimation by constraining the useful interrogation time. We identify spin grid states (SGSs) as the relevant near-optimal probes beyond a crossover at an ensemble size of 51, where GHZ-like states cease to be optimal. SGSs display a periodic grid on the Bloch sphere and can be generated with two one-axis-twisting (OAT) operations separated by a collective rotation. By optimizing the quantum Fisher information over permutationally symmetric states, we find that SGSs perform close to the globally optimal probes for intermediate and large ensembles, which turn out to be spin GKP states. We further present a sequential readout strategy that nearly saturates the corresponding quantum Fisher information. This strategy uses an OAT echo to map spontaneous-emission events onto collective rotations, making the corresponding jump sectors distinguishable and allowing the measurement basis to be conditioned on the number of decay events. Together, these results show that SGSs provide a practical route to quantum-enhanced phase and frequency metrology in atomic ensembles limited by spontaneous emission.
Comments22 pages, 6 figures
