Resonances arising from ion confinement in hybrid atom-ion systems

Current collisional theories for the scattering of a neutral atom with a trapped ion do not account for the confinement of the ion. We present a one-dimensional toy model treating the collisions of free atoms with trapped ions at ultracold temperatures. Our strategy, which treats the trap center as an infinitely massive third particle, is able to capture all dynamical properties of the effective three-body system. The atom-ion pair-wise interaction includes the long-range polarization potential, and an energy-independent quantum defect that accounts for the short-ranged phase of the two-body wavefunction at zero energy. Our calculations reveal the presence of collisional resonances that arise from the trapped states of the atom-ion complex. We provide a brief analysis of these resonances, including their widths and density. Finally, we present preliminary calculations for a more realistic system in three spatial dimensions.