  We demonstrate control of the absolute phase of an optical lattice with
respect to a single trapped ion. The lattice is generated by off-resonant
free-space laser beams, we actively stabilize its phase by measuring its
ac-Stark shift on a trapped ion. The ion is localized within the standing wave
to better than 2\% of its period. The locked lattice allows us to apply
displacement operations via resonant optical forces with a controlled direction
in phase space. Moreover, we observe the lattice-induced phase evolution of
spin superposition states in order to analyze the relevant decoherence
mechanisms. Finally, we employ lattice-induced phase shifts for inferring the
variation of the ion position over 157~$\mu$m range along the trap axis at
accuracies of better than 6~nm.
