This study investigates two-dimensional atom localization controlled by the azimuthal quantum number (l) through the interaction with surface plasmon polaritons (SPPs) in a three-level \(\Lambda \) -type atomic medium. The localization mechanism is governed by the absorption spectrum of SPPs, characterized by the imaginary part of the propagation constant ( \(\textrm{Im}(k_{\textrm{sp}})\) ). We demonstrate that the precise position of atoms can be manipulated by adjusting the azimuthal quantum number and parameters of the applied fields, including probe detuning ( \(\Delta _p\) ), control field detuning ( \(\Delta _1\) ), and decay rates ( \(\gamma _{a,b}\) ). The proposed scheme achieves subwavelength spatial resolution in atom localization, offering potential applications in nanolithography, laser cooling, and atom trapping technologies. These results highlight the significant role of quantum-plasmonic interactions in advanced atomic manipulation techniques.
