Reactive two-body and three-body collisions of Ba${}^{+}$ in an ultracold Rb gas

We analyze reactive collisions of a single Ba${}^{+}$ ion in contact with an ultracold gas of Rb atoms at low three-body collision energies of 2.2(9) mK$\times k_{\mathrm{B}}$. Mapping out the Ba${}^{+}$ loss rate dependence on the Rb atom density we can discern two-body reactive collisions from three-body ones and for the first time determine both rate coefficients which are $k_2=3.1(6)(6)\times {10}^{-13}{\text{cm}}^3{\text{s}}^{-1}$ and $k_3=1.04(4)(45)\times {10}^{-24}{\text{cm}}^6{\text{s}}^{-1}$, respectively (statistical and systematic errors in parenthesis). Thus, the measured ternary recombination dominates over binary reactions even at moderate atom densities of $n\approx {10}^{12}{\text{cm}}^{-3}$. The results for Ba${}^{+}$ and Rb are representative for a wide range of cold ion-atom systems and can serve as a guidance for the future development of the field of hybrid atom-ion research.