We probe small scalar coupling differences via the coherent interactions between two nuclear spin singlet states in organic molecules. We show that the spin-lock induced crossing (SLIC) technique enables the coherent transfer of singlet order between one spin pair and another. The transfer is mediated by the difference in cis and trans vicinal J couplings among the spins. By measuring the transfer rate, we calculate a J coupling difference of $8 pm 2$ mHz in phenylalanine-glycine-glycine and $2.57 pm 0.04$ Hz in glutamate. We also characterize a coherence between two singlet states in glutamate, which may enable the creation of a long-lived quantum memory.
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