In this VAMOS talk I will review recent experiments, in which a trapped-ion, cooled to the ground-state of a Paul trap was interacting with ultracold neutral atoms. When applying the toolbox of trapped-ion quantum computing to these systems, atom-ion interactions can be studied with great sensitivity. In this talk I will review two aspects of ultracold atom-ion interaction that are very different from those of interactions in neutral gasses. The first is that, due to the relatively long-range of the atom-ion polarization potential, the required temperature for s-wave scattering is very low and often out of reach. However, the other side of this long-range interaction, quantum interference effects can be observed at a temperature which is orders of magnitude above the s-wave regime. Secondly, unlike neutral atoms, here the ion is strongly confined by the trap. The presence of the trap for one of the interacting particles breaks translational invariance and leads to the formation of molecules in binary, elastic, collisions.
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