Controlled charge exchange between alkaline earth metals and their ions

We theoretically investigate the prospects of realizing controlled charge exchange via magnetic Feshbach resonances in cold and ultracold collisions of atoms and ions. In particular, we focus on near-resonant charge exchange in heteroisotopic combinations of alkaline earth metals, such as $^9\mathrm{Be}^{+} + ^{10}\mathrm{Be}\leftrightarrow^{9}\mathrm{Be} + ^{10}\mathrm{Be}^{+}$, which exhibit favorable electronic and hyperfine structure. The quantum scattering calculations are performed for a range of initial states and experimentally attainable magnetic fields in standard coupled-channel Feshbach projection formalism, where higher-order corrections such as the mass-polarization term are explicitely included. In addition, we predict a number of magnetic Feshbach resonances for different heteronuclear isotopic combinations of the listed and related alkaline earth elements. Our results imply that near-resonant charge-exchange could be used to realize atom-ion quantum gates, as well as controlled charge transfer in optically trapped cold quantum gases.