Multichannel quantum-defect theory of ultracold atom-ion collisions

We study atom-ion scattering in the ultracold regime. To this aim, an analytical model based on the multichannel quantum defect formalism is developed and compared to close-coupled numerical calculations. We apply our model to the specific systems of ${}^{40}$Ca$^{+}$ - Na and ${}^{138}$Ba$^{+}$ - ${}^{87}$Rb, and investigate the occurrence of magnetic Feshbach resonances. The presence of several resonances at experimentally accessible magnetic fields should allow the atom-ion interaction to be precisely tuned. A fully quantum-mechanical study of charge exchange processes shows that charge-exchange rates should remain small even in the presence of resonance effects. Most of our results can be cast in a system-independent form and are important for the realization of the charge-neutral ultracold systems.