Nuclear spin conservation enables state-to-state control of ultracold molecular reactions.

Quantum-state control of reactive systems has enabled microscopic probes of underlying interaction potentials and the alteration of reaction rates using quantum statistics. However, extending such control to the quantum states of reaction outcomes remains challenging. Here, we realize this goal by utilizing the conservation of nuclear spins throughout the reaction. Using resonance-enhanced multiphoton ionization spectroscopy to investigate the products formed in bimolecular reactions between ultracold KRb molecules we find that the system retains a near-perfect memory of the reactants' nuclear spins, manifested as a strong parity preference for the rotational states of the products. We leverage this effect to alter the occupation of these product states by changing the coherent superposition of initial nuclear spin states with an external magnetic field. In this way, we are able to control both the inputs and outputs of a reaction with quantum-state resolution. The techniques demonstrated here open up the possibilities to study quantum entanglement between reaction products and ultracold reaction dynamics at the state-to-state level.