# A Method for Measurement of Spin-Spin Couplings with sub-mHz Precision Using Zero- to Ultralow-Field Nuclear Magnetic Resonance

## TL;DR

This paper introduces a numerical method for extracting precise spin-spin coupling constants from zero- to ultralow-field NMR data, achieving sub-mHz accuracy and enabling advanced physics experiments.

## Contribution

The paper presents a novel numerical density matrix simulation approach for fitting ZULF NMR spectra to accurately measure J-couplings with unprecedented precision.

## Key findings

- Achieved J-coupling measurement precision of 10^{-2} to 10^{-4} Hz.
- Improved agreement with previous research for most J-couplings.
- Enabled new precision experiments for spin-dependent interactions.

## Abstract

We present a method which allows for the extraction of physical quantities directly from zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) data. A numerical density matrix evolution is used to simulate ZULF NMR spectra of several molecules in order to fit experimental data. The method is utilized to determine the indirect spin-spin couplings ($J$-couplings) in these, which is achieved with precision of $10^{-2}$--$10^{-4}$ Hz. The simulated and measured spectra are compared to earlier research. Agreement and precision improvement for most of the $J$-coupling estimates are achieved. The availability of an efficient, flexible fitting method for ZULF NMR enables a new generation of precision-measurement experiments for spin-dependent interactions and physics beyond the Standard Model.