Magic Polarization for Optical Trapping of Atoms without Stark-Induced Dephasing

We demonstrate that the differential ac-Stark shift of a Zeeman-sensitive ground hyperfine transition in an optical trap can be eliminated by using properly polarized trapping light. We use the vector polarizability of an alkali-metal atom to produce a polarization-dependent ac-Stark shift that resembles a Zeeman shift. We study a transition from the vertical bar 2S(1/2), F = 2, m(F) = -2 > to the vertical bar 2S(1/2,) F = 1, m(F) = -1 > state of Li-7 to observe 0.59 +/- 0.02 Hz linewidth with interrogation time of 2 s and 0.82 +/- 0.06 s coherence time of a superposition state. Implications of the narrow linewidth and the long coherence time for precision spectroscopy and quantum information processing using atoms in an optical lattice are discussed.