Surface Plasmon Polariton-Enhanced Multi-Wave Mixing for Topological 3D Atomic Localization in an Atomic Media

This work examines the 3D localization microscopy of atoms through a new technique employing absorption spectroscopy within a four-level atomic system under multi-wave mixing (MWM) conditions, combined with surface plasmon polaritons (SPPs). The method facilitates the determination of cylindrical and ellipsoidal atomic localization patterns, as well as the realization of one and two atom localization microscopy. The detuning, intensity, phase, and orientation of the applied driving fields are adjusted to precisely control and modulate the probability distribution of localized atoms. The spatial confinement and transitions between distinct localization patterns are significantly influenced by these parameters, which provide a high degree of modification and tunability. The results also illustrate the formation of ellipsoidal localizations across multiple quadrants, as well as the controllable shifting between two localized cylindrical patterns and a unified single-cylinder structure. The findings of this study have the potential to considerably accelerate the development of applications in laser cooling and quantum information processing.