  We demonstrate that the coherence of a single mobile atomic qubit can be well
preserved during a transfer process among different optical dipole traps
(ODTs). This is a prerequisite step in realizing a large-scale neutral atom
quantum information processing platform. A qubit encoded in the hyperfine
manifold of $^{87}$Rb atom is dynamically extracted from the static quantum
register by an auxiliary moving ODT and reinserted into the static ODT.
Previous experiments were limited by decoherences induced by the differential
light shifts of qubit states. Here we apply a magic-intensity trapping
technique which mitigates the detrimental effects of light shifts and
substantially enhances the coherence time to $225 \pm 21\,\mathrm{ms}$. The
experimentally demonstrated magic trapping technique relies on the previously
neglected hyperpolarizability contribution to the light shifts, which makes the
light shift dependence on the trapping laser intensity to be parabolic. Because
of the parabolic dependence, at a certain "magic" intensity, the first order
sensitivity to trapping light intensity variations over ODT volume is
eliminated. We experimentally demonstrate the utility of this approach and
measure hyperpolarizability for the first time. Our results pave the way for
constructing a scalable quantum-computing architectures with single atoms
trapped in an array of magic ODTs.
