Controlled Formation of Ultracold Diatoms via Laser Catalysis: $^6$Li$^6$Li+$^7$Li

Laser catalysis techniques are applied to the quantum control of an ultracold $^6$Li$^6$Li$^7$Li collinear collision on the $1^4A'$ electronic potential energy surface via a fermion-boson light-induced exchange reaction, $^7{\rm Li}^6\textrm{Li} (^3\Sigma^+)$$+^6{\rm Li}(^2S) \stackrel{\hbar\omega_0}{\longleftrightarrow}(^7{\rm Li}^6{\rm Li}^6{\rm Li})^* \stackrel{\hbar\omega_0}{\longleftrightarrow}$ $^6\textrm{Li}_2(^3\Sigma_u^+)$ $+^7\textrm{Li}(^2S)$. We show that the cold ($T_r\approx 1.75$ K) reactant $^6$Li+$^6$Li$^7$Li, when optically coupled to the intermediate bound states on the $1^4A''$ electronic potential energy surface, can be transferred to the ultracold ($0.01$ mK $