A directly observable, Zeeman-insensitive nuclear spin coherence in solution

Clock transitions are well known in atomic and solid-state systems, but are largely unexplored in molecular liquids. Here we demonstrate a clock-like, nuclear-spin avoided crossing in [1–${}^{13}$C]-fumarate that supports long-lived and directly observable coherences at ultralow magnetic field: a three-spin transition $\mathrm{\mid }{S}_0\alpha ⟩\leftrightarrow \mathrm{\mid }{T}_{+1}\beta ⟩$ near 400 nT exhibits a shallow crossing with a frequency minimum of 2 Hz. The transition is first-order immune to magnetic field perturbations and displays a lifetime of 25 s, around three times the longest single-spin $T_2^{\ast }$. Sensitivity to effective pseudo-fields is also demonstrated, including the internal dipolar field of the sample.