Extended Data Fig. 3: Potential energy curves for a Ba⁺ ion interacting with a Li atom.

The interaction between ground-state Ba⁺ ion and Li atom results in two molecular electronic states of the singlet \({X}^{1}{\Sigma }^{+}\) (solid black line) and triplet \({a}^{3}{\Sigma }^{+}\) (solid red line) symmetries. The excited molecular electronic state of the triplet \({b}^{3}\Pi \) symmetry (dashed red line) originates from the interaction of Ba⁺ ion in the lowest excited \({}^{2}D\) state and ground-state Li atom and crosses the \({a}^{3}{\Sigma }^{+}\) state at a small interatomic distance. This crossing combined with SOC between \({a}^{3}{\Sigma }^{+}\) and \({b}^{3}\Pi \) states results in large second-order SOC in the collision channels responsible for the observed Feshbach resonances. Further illustrated is a possible photodissociation transition induced by our xODT laser operated at 1064 nm. The observed TBR might result in the formation of weakly-bound molecular ions. These can couple by laser light to higher energetic asymptotes, resulting in the population of excited states, including Ba \({}^{+}(5{{\rm{D}}}_{5/2})\).