Ultracold collisions of a neutral atom with a trapped ion in one dimension

We present a fully quantum mechanical description of a free $^{6}\mathrm{Li}$ atom scattering from a trapped $^{171}\mathrm{Yb}^{+}$ ion in one dimension. By reformulating the system in polar coordinates and employing the adiabatic representation, we extract a set of coupled adiabatic potentials representing the atom interacting with the ion in different trap states. In an approach similar to quantum defect theory, we leverage the vast difference in energy scale between the interaction, the trap, and the scattering energy to encapsulate the short-range atom-ion scattering behavior in a single phase parameter. The presence of trapped ${(^{171}\mathrm{Yb}^{6}\mathrm{Li})}^{+}$ molecular-ion states leads to a series of roughly evenly spaced resonances in the scattering cross section. The predicted distribution of resonances at low collision energies is at odds with the expectation of quantum chaos and the Bohigas-Giannoni-Schmit conjecture.