A scheme for two-dimensional (2D) atom localization via probe absorption in a three-level $\ensuremath{\Lambda}$-type atomic system is suggested. The required atom-field configuration is obtained when the atom interacts with a weak probe field and two orthogonal standing-wave fields where each standing-wave field is obtained from the superposition of the two standing-wave fields along the corresponding directions. We study the effect of the probe field detuning and phase shifts associated with the standing-wave fields. Two equally probable position information of the single atom are observed in the conditional position probability distribution. However, a unique position of the single atom in the 2D
xy plane is observed for some arbitrary choices of the phases associated with standing-wave fields and by selecting slightly different wavelengths of standing-wave fields.
The localization of atom is studied in two-dimensional (2D) in a four-level V-type atomic system by using the Gaussian field. The atom localization is investigated through the absorption spectrum of the weak probe field inside two orthogonal standing-wave fields. We consider three hypotheses for the interaction between the atom and fields (standing-wave and Gaussian fields), each hypothesis is considered individually. We obtain the expression for the first-order approximation of the absorption of the probe field mathematically for the hypothesis (I). The Gaussian field parameter plays an important role in the precision of the atom localization. The 2D atom localization can be dependent on the detuning of the probe field (resonance and off-resonance), the Rabi frequencies and the phase shifts.