Enhanced atomic localization via surface plasmons at the interface of sodium and multi-walled carbon nanotubes

Two-dimensional atomic microscopy is governed by the dispersion relation of surface plasmon polariton (SPP) waves at the interface between sodium metal and multi-walled carbon nanotubes (MWCNTs). The absorption or damping spectrum of these SPP waves encodes critical information about atomic localization. In accordance with Heisenberg microscopy, atoms can be localized with a resolution of $\lambda /2$ along any spatial axis (x, y, or z). In this study, we tune the dispersion relation of SPPs by adjusting control fields and the parameters of MWCNTs. By adjusting these parameters, we achieve control over the number and positioning of single, double, and multiple localized peaks within a single wavelength domain $(-\pi \leq k_{x} \leq \pi , -\pi \leq k_{y} \leq \pi )$ in the damping spectrum of SPPs on a two-dimensional plane. Notably, we demonstrate atomic localization at scales significantly smaller than $\lambda /2$ , with peak widths reduced to below $\lambda /1000$ along both x- and y-axes. Furthermore, we manipulate the shape and arrangement of localization peaks, achieving loop-like, wall-like, crater-like, and Gaussian profiles. These advancements have potential applications in high-precision atomic position measurement, nano-lithography, and Bose-Einstein condensation.