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We present a theoretical investigation of coherent dynamics of a spin qubitencoded in hyperfine sublevels of an alkali-metal atom in a far off-resonantoptical dipole trap. The qubit is prepared in the "clock transition" utilizingthe Zeeman states with zero projection of the spin angular momentum. We focuson various dephasing processes such as the residual motion of the atom,fluctuations of the trapping field and its incoherent scattering and theireffects on the qubit dynamics. We implement the most general fully-quantumtreatment of the atomic motion, so our results remain valid in the limit ofclose-to-ground-state cooling with low number of vibrational excitations. Wesupport our results by comparison with an experiment showing reasonablecorrespondence with no fitting parameters.

Dynamics of a spin qubit in an optical dipole trap