Two-dimensional atomic localization is governed by the dispersion relation of surface plasmon polariton (SPP) waves at the interface between sodium metal and multi-walled carbon nanotubes. The absorption or damping spectrum of the SPP waves encodes critical information regarding atom localization. Consistent with Heisenberg microscopy, atoms can be localized with a precision of \(\lambda /2\) along any direction of the x, y, or z-axes. External control fields and the intrinsic parameters of the carbon nanotubes influence the dispersion relation of SPP waves. By modulating these control fields and parameters, it is possible to regulate the formation of single, double, or multiple localized peaks within one wavelength domain of \(-\pi \le k_x \le \pi \) and \(-\pi \le k_y \le \pi \) in the damping spectrum of SPPs on a two-dimensional plane. The atom localization region is refined to dimensions significantly smaller than \(\lambda /2\) , with the width of localization peaks reduced to less than \(\lambda /20\) along both the x- and y-axes. Moreover, this work demonstrates control over various localization patterns, including loop-like, wall-like, crater-like, and Gaussian peak structures. These advancements in localization precision and pattern control hold substantial potential for applications in atomic position measurement, nano-lithography, and Bose-Einstein condensation. This approach underscores the transformative capability of SPP wave manipulation in enhancing atom microscopy and related quantum technologies.
