Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers.

由于近年来表现出的高精度和稳定性，光学原子钟成为精密测量的驱动力。虽然人们设想通过使用纠缠原子来进一步提高稳定性，压缩量子力学投影噪声，但评估总体增益必须纳入原子钟的基本特征。在这里，我们研究了自旋压缩态对于使用典型布朗频率噪声限制激光源运行的时钟的好处。基于光学原子钟闭合伺服环路的分析模型，我们在此报告了给定死区时间和激光噪声下最佳时钟稳定性的定量预测。我们的分析预测与闭合伺服环路的数值模拟非常一致。我们发现，对于具有死区时间的单原子系综的通常循环拉姆齐询问，即使使用当前最稳定的激光自旋挤压也只能提高光学 Sr 晶格时钟中低于约 10000 临界原子数的系综的时钟稳定性。即使未来激光性能提高一个数量级，临界原子数仍然低于 100,000。相比之下，基于较小的、不可扩展的系综的时钟（例如离子时钟）已经可以从当前时钟激光器的压缩状态中受益。