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