Abstract: An optical dipole trap for alkali metal atoms is one of the most useful ways for a precision spectroscopy and a quantum information processing (QIP). We are interested in eliminating differential ac-Stark shift of atoms in the optical trap between the two ground hyperfine levels to obtain narrow line width and long coherence time. We study the polarization dependence of the Stark shift via vector polarizability and controlled the polarization of the trapping field. We carry out a hyperfine spectroscopy between two ground hyperfine states . We expect that the magic polarization brings breakthroughs in precision measurement and quantum information processing.<br><br>