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A single $^{40}$Ca ion is confine in the harmonic potential of a Paul trapand cooled to a temperature of a few mK, with a wave packet of sub-m spatialand sub-m/s velocity uncertainty. Deterministically extracted from the Paultrap, the single ion is propagating over a distance of 0.27 m and detected. Byengineering the ion extraction process on the initial wave packet,theoretically modeling the ion trajectories, and studying experimentally thetime-of-flight distribution, we directly infer the state of the previouslytrapped ion. This analysis allows for accurate remote sensing of the previousmotional excitation in the trap potential, both coherently or incoherently. Ourmethod paves a way to extract, manipulate and design quantum wave packets alsooutside of the Paul trap.

Single Ion Thermal Wave Packet Analyzed Via Time-Of-Flight Detection