Localization of cold $^{87}Rb$ atom within half-wavelength domain

Simulating the cold $^{87}Rb$ atom with a three-level quantum system interacting with two orthogonal standing-wave fields, the localization within half-wavelength domain in the x-y plane is achieved by monitoring the probe absorption. Within the half-wavelength domain, the single absorption peak increases from 0.2 to 1.0 via the spontaneously generated coherence (SGC), while the diameters of the single absorption peaks are diminished by the increasing incoherent pumping field. Our scheme provides the flexible parameters manipulating manner for the localization of cold $^{87}Rb$ atom.