Mode analysis of spin field of thermal atomic ensembles

Abstract

Abstract 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.