  A single Yb atom is loaded into a high-finesse optical cavity with a moving
lattice, and its nuclear spin state is manipulated using a nuclear magnetic
resonance technique. A highly reliable quantum state control with fidelity and
purity greater than 0.98 and 0.96, respectively, is confirmed by the full
quantum state tomography; a projective measurement with high speed (500us) and
high efficiency (0.98) is accomplished using the cavity QED technique. Because
a hyperfine coupling is induced only when the projective measurement is
operational, the long coherence times (T_1 = 0.49 s and T_2 = 0.10 s) are
maintained. Our technique can be applied for implementing a scalable one-way
quantum computation with a cluster state in an optical lattice.
