Ultracold coherent control of molecular collisions at a Förster resonance

We show that the precise microwave preparation of a quantum superposition between three rotational states of an ultracold dipolar molecule generates controllable interferences in their two-body scattering dynamics and collisional rate coefficients, at an electric field that produces a F & ouml;rster resonance. This proposal represents a feasible protocol to achieve coherent control on ultracold molecular collisions in current experiments. It sets the basis for future studies in which one can think to control the amount of each produced pairs, including trapped entangled pairs of reactants, individual pairs of products in a chemical reaction, and measuring each of their scattering phase shifts that could envision "complete chemical experiments" at ultracold temperatures.