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.
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