Microwave control of trapped-ion motion assisted by a running optical lattice.

We experimentally demonstrate microwave control of the motional state of a trapped ion placed in a state-dependent potential generated by a running optical lattice. Both the optical lattice depth and the running lattice frequency provide tunability of the spin-motion coupling strength. The spin-motional coupling is exploited to demonstrate sideband cooling of a ^{171}Yb^{+} ion to the ground state of motion.