The spin dynamics in a thermal atomic vapor cell have been investigated thoroughly over the past decades and have proven to be successful in quantum metrology and memory owing to their long coherent time and manipulation convenience. The existing mean field analysis of spin dynamics among the whole cell is sometimes inaccurate due to the non-uniformity of the ensemble and spatial coupling of multi-physical fields interacting with the ensembles. Here we perform mode analysis onto the quasi-continuous spin field including atomic thermal motion to derive Bloch mode equations and obtain corresponding analytical solutions in diffusion regime. We demonstrate that the widely used mean field dynamics of thermal gas is a particular case in our solution, corresponding to the uniform spatial mode. This mode analysis approach offers a precise method for analyzing the dynamics of the spin ensemble in greater detail from a field perspective, enabling the effective determination of spatially non-uniform multi-physical fields coupling with the spin ensembles, which cannot be accurately analyzed by the mean field method. Furthermore, this work paves the way to address quantum noises and relaxation mechanisms associated with non-uniform fields and inter-atomic interactions, which limit further improvement of ultra-sensitive spin-based sensors.

中文翻译：

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热原子系综自旋场模态分析


过去几十年来，热原子蒸汽电池中的自旋动力学已经得到了彻底的研究，并且由于其长相干时间和操作便利性，已被证明在量子计量和存储领域取得了成功。由于系综的不均匀性以及与系综相互作用的多物理场的空间耦合，现有的全细胞自旋动力学平均场分析有时是不准确的。在这里，我们对包括原子热运动的准连续自旋场进行模式分析，推导布洛赫模式方程并获得扩散区域中相应的解析解。我们证明了广泛使用的热气体平均场动力学是我们解决方案中的一个特例，对应于均匀空间模式。这种模态分析方法提供了一种从场角度更详细地分析自旋系综动力学的精确方法，能够有效确定与自旋系综耦合的空间非均匀多物理场，而这些空间非均匀多物理场无法通过自旋系综进行精确分析。平均场法。此外，这项工作为解决与非均匀场和原子间相互作用相关的量子噪声和弛豫机制铺平了道路，这些机制限制了超灵敏自旋传感器的进一步改进。