  We investigate transport dynamics of a single low-energy ionic impurity in a
Bose-Einstein condensate. The impurity is implanted into the condensate
starting from a single Rydberg excitation, which is ionized by a sequence of
fast electric field pulses aiming to minimize the ion's initial kinetic energy.
Using a small electric bias field, we study the subsequent collisional dynamics
of the impurity subject to an external force. The fast ion-atom collision rate,
stemming from the dense degenerate host gas and the large ion-atom scattering
cross section, allows us to study a regime of frequent collisions of the
impurity within only tens of microseconds. Comparison of our measurements with
stochastic trajectory simulations based on sequential Langevin collisions
indicate diffusive transport properties of the impurity and allows us to
measure its mobility. Furthermore, working with a free and untrapped ion
provides unique means to distinguish single realizations, where the impurity is
subject to inelastic molecular-ion formation via three-body recombination. We
study the cold chemistry of these events and find evidence for subsequent
rovibrational quenching collisions of the produced molecule. Our results open a
novel path to study dynamics of charged quantum impurities in ultracold matter.
