A method for measurement of spin-spin couplings with sub-mHz precision using zero- to ultralow-field nuclear magnetic resonance.

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 systems, which is achieved with precision of 10(-2)-10(-4)Hz. The simulated and measured spectra are compared to earlier research. Agreement and improved precision are achieved for most of the J-coupling estimates. The availability of fast, flexible fitting method for ZULF NMR enables a new generation of precision-measurement experiments for spin-dependent interactions and physics beyond the Standard Model.