The detection of single nuclear spins is an important goal in magnetic resonance spectroscopy. Optically detected magnetic resonance can detect single nuclear spins that are strongly coupled to an electron spin, but the detection of distant nuclear spins that are only weakly coupled to the electron spin has not been considered feasible. Here, using the nitrogen-vacancy centre in diamond as a model system, we numerically demonstrate that it is possible to detect two or more distant nuclear spins that are weakly coupled to a centre electron spin if these nuclear spins are strongly bonded to each other in a cluster. This cluster will stand out from other nuclear spins by virtue of characteristic oscillations imprinted onto the electron spin decoherence profile, which become pronounced under dynamical decoupling control. Under many-pulse dynamical decoupling, the centre electron spin coherence can be used to measure nuclear magnetic resonances of single molecules. This atomic-scale magnetometry should improve the performance of magnetic resonance spectroscopy for applications in chemical, biological, medical and materials research, and could also have applications in solid-state quantum computing.

We theoretically study the decoherence and the dynamical decoupling control of nitrogen-vacancy center electron spins in high-purity diamond, where the hyperfine interaction with 13 C nuclear spins is the dominating decoherence mechanism. The decoherence is formulated as the entanglement between the electron spin and the nuclear spins, which is induced by nuclear spin bath evolution conditioned on the electron spin state. The nuclear spin bath evolution is driven by elementary processes such as single spin precession and pairwise flipflops. The importance of different elementary processes in the decoherence depends on the strength of the external magnetic field.