The \(\Lambda -\Xi\) atomic system is employed to examine the localization behavior of atom in two-dimensional (2D) and three-dimensional (3D) cases. The variation in atom-field interaction across space results in a position-dependent probe susceptibility. This enables the determination of an atom’s position probability distribution through the analysis of probe spectra. We have elucidated the system behavior by scrutinizing the dressed states approach, which provide the fundamental framework for its physical interpretation. High-resolution and precise sub-wavelength atom localization can be attained by properly tuning the system parameters. The implementation of running wave field to create destructive quantum interference phenomenon is pivotal in enhancing the precision and efficiency of locating atomic positions with \(100\%\) probability in 2D and 3D subspaces. We also observe how the Doppler broadening affects atom positioning in both two-dimensional and three-dimensional space. Our findings demonstrate that the Doppler broadening significantly diminishes the accuracy of spatial localization.

\(\Lambda -\Xi\)原子系统用于检查二维 (2D) 和三维 (3D) 情况下原子的局域化行为。空间中原子场相互作用的变化导致探针磁化率依赖于位置。这使得能够通过分析探针光谱来确定原子的位置概率分布。我们通过仔细研究着装状态方法来阐明系统行为，这为其物理解释提供了基本框架。通过适当调整系统参数可以实现高分辨率和精确的亚波长原子定位。实现运行波场产生破坏性量子干涉现象对于提高2D和3D子空间中100%概率原子位置定位的精度和效率至关重要。我们还观察多普勒展宽如何影响二维和三维空间中的原子定位。我们的研究结果表明，多普勒展宽显着降低了空间定位的准确性。