Avoided crossing (LAC) transitions are central to spin-based precision measurements since they provide strong observability and field-perturbation insensitivity, but while observed commonly in isolated-atom or engineered solid-state platforms, such transitions are unexploited in molecules in liquids. Here we report a solution-state, nuclear-spin LAC transition in hyperpolarized [1-
13C]-fumarate. The singlet-triplet LAC, occurring near 400 nT produces pronounced magnetization oscillations at approximately 2 Hz with a coherence time of 25 s, three times longer than the longest single-spin
T2∗. In the regime of high spin concentration and high polarization the sample's internal dipolar field couples measurably to the transition, providing a direct probe of nonlinear spin dynamics. These results establish nuclear-spin LACs as a platform for quantum sensing in liquids.
Quantum control of reactive systems has enabled microscopic probes of underlying interaction potentials, the opening of novel reaction pathways, and the alteration of reaction rates using quantum statistics. However, extending such control to the quantum states of reaction outcomes remains challenging. In this work, we realize this goal through the nuclear spin degree of freedom, a result which relies on 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 superposition of initial nuclear spin states with an external magnetic field. The techniques demonstrated here open up the possibility to study ultracold reaction dynamics at the state-to-state level as well as quantum entanglement between reaction products.