Quantum state dependent chemistry of ultra-cold $^6$Li$_2$ dimers

Starting from an ultra-cold ensemble of $^6$Li$_2$ Feshbach molecules, we produce deeply bound molecules by STIRAP in the lowest energy levels of the $v=0,\; 5,\; 8$ and $9$ vibrational manifolds of the $a(1^3\Sigma_{u}^+)$ potential. The ensemble lifetime is found to be limited by two-body collisions with a loss rate near the universal rate for three of these states and, remarkably, below universality for the $|v=9, N=0\rangle$ state. In addition, unlike all prior experimental work with ultra-cold molecules, we observe a rotational state dependence of the reaction rate. We observe that molecules in the absolute lowest triplet level are unstable. Because of the suppression of spin-changing collisions and absence of other inelastic collision channels, we conclude this instability is primarily due to trimer formation, consistent with theoretical predictions.