Complete Quantum Coherent Control of Ultracold Molecular Collisions

We show that quantum interference-based coherent control is a highly efficient tool for tuning ultracold molecular collision dynamics, and free from the limitations of commonly used methods rely on external electromagnetic fields. By varying {the relative populations and} phases an initial superpositions degenerate states, we demonstrate complete over integral scattering cross sections in $s$-wave regime both final channels. The proposed methodology applied to O$_2$~+~O$_2$ collisions, showing extensive spin-exchange product branching ratios many orders magnitude.