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We investigate the effects of a novel approach to diamond nanofabrication andnitrogen vacancy (NV) center formation on the optical linewidth of the NVzero-phonon line (ZPL). In this post-implantation method, nitrogen is implantedafter all fabrication processes have been completed. We examine threepost-implanted samples, one implanted with $^{14}$N and two with $^{15}$Nisotopes. We perform photoluminescence excitation (PLE) spectroscopy to assessoptical linewidths and optically detected magnetic resonance (ODMR)measurements to isotopically classify the NV centers. From this, we find thatNV centers formed from nitrogen naturally occuring in the diamond lattice arecharacterized by a linewidth distribution peaked at an optical linewidth nearlytwo orders of magnitude smaller than the distribution characterizing most ofthe NV centers formed from implanted nitrogen. Surprisingly, we also observe anumber of $^{15}$NV centers with narrow ($<500\,\mathrm{MHz}$) linewidths,implying that implanted nitrogen can yield NV centers with narrow opticallinewidths. We further use a Bayesian approach to statistically model thelinewidth distributions, to accurately quantify the uncertainty of fitparameters in our model, and to predict future linewidths within a particularsample. Our model is designed to aid comparisons between samples and researchgroups, in order to determine the best methods of achieving narrow NVlinewidths in structured samples.

Statistically Modeling Optical Linewidths of Nitrogen Vacancy Centers in Post-Implanted Nanostructures