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We report on Fourier spectroscopy experiments performed with near-surfacenitrogen-vacancy centers in a diamond chip. By detecting the free precession ofnuclear spins rather than applying a multipulse quantum sensing protocol, weare able to unambiguously identify the NMR species devoid of harmonics. Wefurther show that by engineering different Hamiltonians during free precession,the hyperfine coupling parameters as well as the nuclear Larmor frequency canbe selectively measured with high precision (here 5 digits). The protocols canbe combined to demonstrate two-dimensional Fourier spectroscopy. The techniquewill be useful for mapping nuclear coordinates in molecules en route to imagingtheir atomic structure.

One- and two-dimensional nuclear magnetic resonance spectroscopy with a diamond quantum sensor