title: Phase-Stable Free-Space Optical Lattices for Trapped Ions.
abstract: 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, and 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 the 157  μm range along the trap axis at accuracies of better than 6 nm.
authors: Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany.
authors: C T
authors: CT
authors: Schmiegelow
authors: Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany.
authors: H
authors: H
authors: Kaufmann
authors: Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany.
authors: T
authors: T
authors: Ruster
authors: Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany.
authors: J
authors: J
authors: Schulz
authors: Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany.
authors: V
authors: V
authors: Kaushal
authors: Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany.
authors: M
authors: M
authors: Hettrich
authors: Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany.
authors: F
authors: F
authors: Schmidt-Kaler
authors: Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany.
authors: U G
authors: UG
authors: Poschinger