Dressed state analysis of two- and three-dimensional atom localization in the Λ - Ξ configuration

The Lambda - Xi atomic system is employed to examine the localization behavior of atom in two-dimensional (2D) and threedimensional (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.