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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.
Control over physical systems at the quantum level is a goal shared by scientists in fields as diverse as metrology, information processing, simulation and chemistry. For trapped atomic ions, the quantized motional and internal degrees of freedom can
We implement a two-qubit entangling M{o}lmer-S{o}rensen interaction by transporting two co-trapped $^{40}mathrm{Ca}^{+}$ ions through a stationary, bichromatic optical beam within a surface-electrode Paul trap. We describe a procedure for achieving a
Thermodynamics is one of the oldest and well-established branches of physics that sets boundaries to what can possibly be achieved in macroscopic systems. While it started as a purely classical theory, it was realized in the early days of quantum mec
Trapped-ion quantum information processors offer many advantages for achieving high-fidelity operations on a large number of qubits, but current experiments require bulky external equipment for classical and quantum control of many ions. We demonstra
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