Distributed cavity phase shift analysis of atomic clocks based on intracavity cooling

Distributed cavity phase shift constitutes a significant source of frequency uncertainty in cold-atom microwave frequency standards and presents challenges in the miniaturization process of high-performance atomic clocks. This paper introduces a method for calculating the distributed cavity phase shift utilizing 3D finite element simulation and Monte Carlo traversal of atoms. The impact of the distributed cavity phase shift on the miniaturized atomic clock is analytically calculated. Results demonstrate that the uncertainties of the distributed cavity phase shift are superior to 2×10-16 at varying atomic temperatures when the Ramsey line width is 10 Hz. Consequently, the long-term stability of this miniaturized atomic frequency standard scheme will not be constrained by the distributed-cavity phase shift, offering a notable advantage in long-term performance among miniaturized atomic clocks. The calculation method can also be extended to rectangular cavities, loop-gap cavities, and in-situ probing microwave cavities with complex structures, proving invaluable for analyzing the distributed cavity phase shift of atomic clocks and optimizing microwave cavity design.

分布腔相移（Distributed cavity phase shift）是冷原子微波频率基准中一项重要的频率不确定度来源，同时给高性能原子钟的小型化进程带来了显著挑战。本文提出一种基于三维有限元仿真与原子蒙特卡洛遍历的分布腔相移计算方法，并对分布腔相移对小型化原子钟的影响开展了解析计算。结果显示，当拉姆齐线宽为10 Hz时，在不同原子温度条件下，分布腔相移的不确定度均优于2×10^-16。据此，该小型化原子频率基准方案的长期稳定性不会受分布腔相移的制约，在小型化原子钟的长期性能表现中具备显著优势。该计算方法还可推广应用至矩形腔、环路间隙腔以及结构复杂的原位探测微波腔，对于分析原子钟的分布腔相移、优化微波腔设计具有重要的应用价值。