Landau quantization effects in ultracold atom-ion collisions

We study ultracold atom-ion collisions in the presence of an external magnetic field. At low collision energy the field can drastically modify the translational motion of the ion, which follows quantized cyclotron orbits. We present a rigorous theoretical approach for the calculation of quantum scattering amplitudes in these conditions. Collisions in different magnetic field regimes, identified by the size of the cyclotron radius with respect to the range of the interaction potential, are investigated. Our results are important in cases where use of a magnetic field to control the atom-ion collision dynamics is envisioned.