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Research for cooling and trapping of atoms in the mid 1980s was mainly motivated to enableprecise spectroscopic measurement. However, perturbation by the trapping force introduces sig-nicant inhomogeneous broadening, and the long interrogation time did not directly translate intonarrow lines. We have devised methods to eliminate the broadening in both optical and groundhyperne transitions of alkali metal atoms by using magic wavelength and magic polarization, re-spectively. I will discuss our experiments on cesium atoms using magic wavelength, and on lithiumatoms using magic polarization. In addition, the narrow hyperne transition of lithium atoms,which are trapped in a 1D optical lattice with magic polarization, allows site-specic addressing when a magnetic eld gradient is applied. I will talk about our experiment to manipulate two single atoms - or qubits - in adjacent sites of the lattice in a coherent and independent way. Host: Marco Cerezo |