Optical coherence of diamond nitrogen-vacancy centers formed by ion implantation and annealing

The advancement of quantum optical science and technology with solid-state emitters such as nitrogen-vacancy (NV) centers in diamond critically relies on the coherence of the emitters' optical transitions. A widely employed strategy to create NV centers at precisely controlled locations is nitrogen ion implantation followed by a high-temperature annealing process. We report on experimental data directly correlating the NV center optical coherence to the origin of the nitrogen atom. These studies reveal low-strain, narrow-optical-linewidth $(<500$ MHz) NV centers formed from naturally occurring ${}^{14}\mathrm{N}$ atoms. In contrast, NV centers formed from implanted ${}^{15}\mathrm{N}$ atoms exhibit significantly broadened optical transitions $(>1$ GHz) and higher strain. The data show that the poor optical coherence of the NV centers formed from implanted nitrogen is not due to an intrinsic effect related to the diamond or isotope. These results have immediate implications for the positioning accuracy of current NV center creation protocols and point to the need to further investigate the influence of lattice damage on the coherence of NV centers from implanted ions.

Figure 1

NV creation via nitrogen-ion implantation. (a) Schematic showing implanted ${}^{15}\mathrm{N}^{+}$ ions (orange) leaving a trail of vacancies (purple) until settling into a final position. Naturally abundant ${}^{14}\mathrm{N}$ ions (green) are shown randomly distributed throughout the diamond lattice. Vacancies (implantation-induced or native) mobilized by annealing can bind to a nitrogen atom (implanted or native). (b) A SRIM simulation using the parameters in sample A show the distribution of implanted nitrogen (orange) and created vacancies (purple). The shaded green area indicates the range of the estimated natural ${}^{14}\mathrm{N}$ concentration reported by Element 6.

Figure 2

Isotope characterization and optical measurements of NV centers from ${}^{14}\mathrm{N}$ and ${}^{15}\mathrm{N}$. (a) A fluorescent confocal scan of sample A taken at 4 K, with labels indicating NV centers characterized as ${}^{14}\mathrm{NV},{}^{15}\mathrm{NV}$, and a set with unresolvable hyperfine lines, labeled as ${}^{?}\mathrm{NV}$. A scan a few microns below the implanted layer (inset) shows a lower NV density. (b)–(d) Pulse sequences (top row) used for isotope characterization and optical measurements, and representative measurement results for each isotope (green, middle row: ${}^{14}\mathrm{NV}$; orange, bottom row: ${}^{15}\mathrm{NV})$. (b) Continuous-wave ODMR measurements reveal the NV isotope. The ${}^{14}\mathrm{NV}$ is characterized by $S=1$ hyperfine transitions; the ${}^{15}\mathrm{NV}$ by $S=1/2$ hyperfine transitions. (c) Interleaved red and green excitation probe the combined effect of short-timescale fluctuations and laser-induced spectral diffusion. The $E_x$ and $E_y$ ZPL transitions are visible for both isotopes; the ${}^{14}\mathrm{NV}$ linewidths are narrower and show a smaller strain splitting than the ${}^{15}\mathrm{NV}$. (d) Individual line scans of the ZPL in sample B reveal the linewidth free from laser-induced spectral diffusion. The summation of many repeated scans is broadened as a result of repump-laser-induced spectral diffusion.

Figure 3

Optical linewidths per isotope. (a), (b) A summary of the optical linewidths identified in sample A (a) and sample B (b) from scans at the implantation depth. For sample B, that has comparatively few ${}^{14}\mathrm{NV}$ centers at the implantation depth, we included three ${}^{14}\mathrm{NV}$ centers found deeper in the diamond to enable a comparison between NVs formed from implanted versus native nitrogen. The distribution is represented as a cumulative distribution function (CDF, top), with the corresponding histogram shown below. The shaded region in the CDF indicates a 95% confidence interval calculated using Greenwood's formula. These data show that both diamonds supported narrow-linewidth NV centers, the majority of which originated from ${}^{14}\mathrm{NVs}$. While ${}^{15}\mathrm{NV}$ do exhibit narrow lines, their median linewidth (M) is higher than for the ${}^{14}\mathrm{NV}$ centers in both samples. We evaluate the probability to obtain the observed linewidths for ${}^{14}\mathrm{NV}$ centers and ${}^{15}\mathrm{NV}$ centers if the samples are drawn from the same distribution with a Wilcoxon rank sum test, finding a $p$ value of $2.5\times {10}^{-4}$ in sample A and $1.7\times {10}^{-3}$ in sample B. (c), (d) A magnification of the histograms shown in (a) and (b).

Figure 4

Strain analysis. (a), (b) The distribution of axial strain (measured by absolute average ZPL frequency) in NVs acquired from analysis of sample A (a) and sample B (b). The ${}^{15}\mathrm{NV}$ ZPLs exhibit a larger spread in axial strain (standard deviation, $\sigma )$ than the ${}^{14}\mathrm{NV}$ ZPLs. (c), (d) The distribution of transverse strain (measured by half the splitting between $E_x$ and $E_y$ frequencies) in NV centers of sample A (c) and sample B (d). The ${}^{15}\mathrm{NV}$ ZPLs show a greater median splitting (M) in both samples.