Mode Analysis of Spin Field of Thermal Atomic Ensembles

Abstract The spin dynamics in a thermal atomic vapor cell have been investigated thoroughly over the past decades and have proven 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-uniform 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 show 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 details from a field perspective, enabling the effective determination of spatially non-uniform multi-physical field coupling with the spin ensembles, which cannot be accurately analyzed by the mean field method. Furthermore, this work paves a way to address noises and relaxation mechanisms associated with non-uniform fields and interatomic interactions, which are limiting the further improvement of ultrasensitive spin-based sensors.