Abstract
We present theoretical proposals for two-dimensional nuclear magnetic resonance spectroscopy protocols based on Nitrogen-vacancy (NV) centers in diamond that are strongly coupled to the target nuclei. Continuous microwave and radio-frequency driving fields together with magnetic field gradients achieve Hartmann-Hahn resonances between NV spin sensor and selected nuclei for control of nuclear spins and subsequent measurement of their polarization dynamics. The strong coupling between the NV sensor and the nuclei facilitates coherence control of nuclear spins and relaxes the requirement of nuclear spin polarization to achieve strong signals and therefore reduced measurement times. Additionally, we employ a singular value thresholding matrix completion algorithm to further reduce the amount of data required to permit the identification of key features in the spectra of strongly sub-sampled data. We illustrate the potential of this combined approach by applying the protocol to a shallowly implanted NV center addressing a small amino acid, alanine, to target specific hydrogen nuclei and to identify the corresponding peaks in their spectra.