Phase-stable free-space optical lattices for trapped ions

TL;DR

This paper demonstrates phase control of a free-space optical lattice for trapped ions, enabling precise manipulation and measurement of ion position and coherence with high stability and accuracy.

Contribution

It introduces a method to actively stabilize the phase of an optical lattice relative to a trapped ion, enhancing control for quantum information applications.

Findings

Achieved ion localization within 2% of the lattice period.

Controlled displacement operations in phase space.

Inferred ion position variation with better than 6 nm accuracy.

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, 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.