Statistically modeling optical linewidths of nitrogen vacancy centers in microstructures

Abstract

We investigate the relationship between ion implantation and the optical linewidth of the nitrogen vacancy (NV) zero-phonon line (ZPL) in bulk and structured samples. We also propose a novel approach to ion implantation that we name postimplantation, in which nitrogen is implanted after all fabrication processes have been completed. We examine three post-implanted samples, one implanted with $^{14}\mathrm{N}$ and two with $^{15}\mathrm{N}$ isotopes. We perform photoluminescence excitation (PLE) spectroscopy to assess optical linewidths and optically detected magnetic resonance (ODMR) measurements to isotopically classify the NV centers. From this, we find that NV centers formed from nitrogen naturally occurring in the diamond lattice are characterized by a linewidth distribution peaked at an optical linewidth nearly two orders of magnitude smaller than the distribution characterizing most of the NV centers formed from implanted nitrogen. Surprisingly, we also observe a number of $^{15}\mathrm{NV}$ centers with narrow ($<500\phantom{\rule{4pt}{0ex}}\mathrm{MHz}$) linewidths, implying that implanted nitrogen can yield NV centers with narrow optical linewidths. We further use a Bayesian approach to statistically model the linewidth distributions, to accurately quantify the uncertainty of fit parameters in our model, and to predict future linewidths within a particular sample. Our model is designed to aid comparisons between samples and research groups, in order to determine the best methods of achieving narrow NV linewidths in structured samples.