Quadrature-detected zero-to-ultralow-field nuclear magnetic resonance

We present the concept of quadrature-detected zero-to-ultralow-field nuclear magnetic resonance (QD ZULF NMR). Two orthogonal sensors, atomic optically pumped magnetometers, are used to separately detect components of oscillating sample magnetization, which are then combined into a quadrature signal. This approach enables the distinction of positive and negative resonance frequencies with respect to the laboratory frame—such that absolute signs of gyromagnetic ratios can be determined. In addition, QD ZULF NMR reduces peak density and overlap compared to ZULF NMR with single-axis detection, while providing richer information about nuclear-spin dynamics. As an illustration, we present experimental $J$-spectra for thermally polarized [${}^{13}$C]-formic acid and [${}^{13}$C]-methanol, compounds commonly used in ZULF NMR which represent XA and XA${}_3$ spin systems, respectively. A theoretical framework describing QD ZULF NMR signals is provided.