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Atomic clocks based on an Al$^+$ ion sympathetically cooled by a laser-cooledalkaline-earth ion have achieved unprecedented accuracy. Here, we investigatetheoretically interactions and charge transfer dynamics of an Al$^+$ ionimmersed in an ultracold gas of Rb and Sr atoms. We calculate potential energycurves and transition electric dipole moments for the (Al+Rb)$^+$ and(Al+Sr)$^+$ ion-atom systems using coupled cluster and multireferenceconfiguration interaction methods with scalar relativistic effects includedwithin the small-core energy-consistent pseudopotentials in Rb and Sr atoms.The long-range interaction coefficients are also reported. We use theelectronic structure data to investigate cold collisions and charge transferdynamics. Scattering of an Al$^+$ ion with alkali-metal or alkaline-earth-metalatom is governed by one potential energy curve whereas charge transfer can leadto several electronic states mixed by the relativistic spin-orbit coupling. Weexamine the branching ratios resulting from the interplay of the short- andlong-range effects, as well as the prospects for the laser-field control andformation of molecular ions. We propose to employ the atomic clock transitionin an Al$^+$ ion to monitor ion-atom scattering dynamics via quantum logicspectroscopy. The presented results pave the way for the application of atomicions other than alkali-metal and alkaline-earth-metal ones in the field of coldhybrid ion-atom experiments.

Interactions and charge transfer dynamics of an Al$^+$ ion immersed in ultracold Rb and Sr atoms