We present a comprehensive theoretical investigation of two-dimensional (2D) Compton-azimuthal atomic localization in a three-level atomic system interacting with spatially structured light fields. The study focuses on how the azimuthal quantum numbers of the applied standing-wave fields influence the spatial probability distribution of an atom within the 2D plane. By numerically solving the governing equations of motion with realistic atomic parameters, we obtain localization maps that reveal sharp and well-defined probability peaks. The spatial localization arises from the position-dependent Rabi frequencies, which are modulated by the standing-wave interference patterns and the orbital angular momentum carried by the fields. Our results demonstrate a clear transition from multiple sharp localization peaks to a single dominant peak as ℓ1 and ℓ2 are reduced. This peak reduction significantly increases the probability of finding the atom at the remaining high-probability sites, reaching 100% localization probability in the single-peak regime. Physically, this occurs because lower azimuthal mode numbers simplify the spatial interference structure, concentrating the atomic wavefunction in a narrower spatial region. The tunability of localization via ℓ1 and ℓ2 provides a flexible control mechanism for atomic position measurement with subwavelength precision. The findings not only offer new insights into Compton-azimuthal localization mechanisms but also open potential applications in quantum metrology, atom-based nanolithography, and precision quantum control of matter–light interactions in structured optical fields.
Kalsoom et al. (Wed,) studied this question.