  We present a theoretical investigation of coherent dynamics of a spin qubit
encoded in hyperfine sublevels of an alkali-metal atom in a far off-resonant
optical dipole trap. The qubit is prepared in the "clock transition" utilizing
the Zeeman states with zero projection of the spin angular momentum. We focus
on various dephasing processes such as the residual motion of the atom,
fluctuations of the trapping field and its incoherent scattering and their
effects on the qubit dynamics. We implement the most general fully-quantum
treatment of the atomic motion, so our results remain valid in the limit of
close-to-ground-state cooling with low number of vibrational excitations. We
support our results by comparison with an experiment showing reasonable
correspondence with no fitting parameters.
