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.

中文翻译：

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通过驻波和高斯场的组合进行二维原子定位

利用高斯场在四能级V型原子系统中二维（2D）研究原子的定位。通过两个正交驻波场内的弱探针场的吸收光谱来研究原子定位。我们考虑了原子和场（驻波场和高斯场）之间相互作用的三个假设，每个假设都是单独考虑的。对于假设 (I)，我们在数学上获得了探测场吸收的一阶近似表达式。高斯场参数对原子定位的精度起着重要作用。2D 原子定位可能取决于探针场的失谐（共振和非共振）、拉比频率和相移。