Atomic-scale imaging of a 27-nuclear-spin cluster using a single-spin quantum sensor

Nuclear magnetic resonance (NMR) is a powerful method for determining the structure of molecules and proteins. While conventional NMR requires averaging over large ensembles, recent progress with single-spin quantum sensors has created the prospect of magnetic imaging of individual molecules. As an initial step towards this goal, isolated nuclear spins and spin pairs have been mapped. However, large clusters of interacting spins - such as found in molecules - result in highly complex spectra. Imaging these complex systems is an outstanding challenge due to the required high spectral resolution and efficient spatial reconstruction with sub-angstrom precision. Here we develop such atomic-scale imaging using a single nitrogen-vacancy (NV) centre as a quantum sensor, and demonstrate it on a model system of $27$ coupled $^{13}$C nuclear spins in a diamond. We present a new multidimensional spectroscopy method that isolates individual nuclear-nuclear spin interactions with high spectral resolution ($< 80\,$mHz) and high accuracy ($2$ mHz). We show that these interactions encode the composition and inter-connectivity of the cluster, and develop methods to extract the 3D structure of the cluster with sub-angstrom resolution. Our results demonstrate a key capability towards magnetic imaging of individual molecules and other complex spin systems.