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We analyze reactive collisions of a single Ba$^+$ ion in contact with anultracold 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 theRb atom density we can discern two-body reactive collisions from three-bodyones and for the first time determine both rate coefficients which are$k_2=3.1(6)(6)\times 10^{-13}\textrm{cm}^{3}\textrm{s}^{-1}$ and$k_3=1.04(4)(45)\times 10^{-24}\textrm{cm}^{6}\textrm{s}^{-1}$, respectively(statistical and systematic errors in parenthesis). Thus, the measured ternaryrecombination dominates over binary reactions even at moderate atom densitiesof $n\approx 10^{12}\: \textrm{cm}^{-3}$. The results for Ba$^+$ and Rb arerepresentative for a wide range of cold ion-atom systems and can serve as aguidance for the future development of the field of hybrid atom-ion research.

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