Figure 3: NV gradient separation of individual ²⁹Si nuclei.

(a) Under high-order decoupling (XY8-512 pulse sequence), inhomogeneous broadening of the ²⁹Si NMR line due to the NV magnetic gradient can be observed. The expected line width of the XY8-512 sequence for weakly interacting nuclear spins is shown as the black dotted line with a FWHM of 6 kHz. The blue solid line is the best fit to the data using basis pursuit (see Supplementary Note 7 for technical details) showing an additional broadening of 4 kHz. (b) Using BPDN, we calculate the Larmor frequency and relative contribution of 50 nuclear spins comprising the total signal (see Methods). These are plotted individually, with the four strongest highlighted, which contribute to more than 50% of the signal.