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

TL;DR

This study investigates how the optical coherence of nitrogen-vacancy centers in diamond depends on their nitrogen source, revealing that naturally-occurring nitrogen yields better coherence than implanted nitrogen, impacting quantum technology applications.

Contribution

The paper provides direct experimental evidence linking NV center optical coherence to nitrogen origin, highlighting the effects of implantation versus natural incorporation.

Findings

Naturally-occurring $^{14}$N NV centers have narrow linewidths (<500 MHz).

Implanted $^{15}$N NV centers show broader linewidths (>1 GHz).

Poor coherence from implanted nitrogen is not due to intrinsic diamond properties.

Abstract

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 $^{14}$N atoms. In contrast, NV centers formed from implanted $^{15}$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.

Full text

Coherent optical control over solid-state quantum emitters has enabled new advances in quantum science (Aharonovich et al., 2016; Awschalom et al., 2018; Lodahl, 2018) and may lead to technologies such as quantum networks (Wehner et al., 2018). A quantum network crucially relies on entanglement connections that can be established through a coherent spin-photon interface. The nitrogen-vacancy (NV) defect center in diamond is a well-suited candidate owing to a spin ground state with a long coherence time (Bar-Gill et al., 2013; Abobeih et al., 2018), nearby nuclear spins for quantum memories (Kalb et al., 2017) or algorithms (Waldherr et al., 2014; Cramer et al., 2016; Lovchinsky et al., 2016), and spin-selective optical transitions allowing for efficient optical spin initialization and readout (Robledo et al., 2011). Moreover, at low strain and low temperature ($<10$ K), effects from phonon mixing in the excited state are small (Fu et al., 2009; Goldman et al., 2015), and the optical transition can be coherent. Indeed, narrow-linewidth, coherent optical transitions (Tamarat et al., 2006; Batalov et al., 2008; Robledo et al., 2010) have been used for the generation of indistinguishable photons suited for two photon quantum interference (Bernien et al., 2012; Sipahigil et al., 2012) and entanglement generation between remote NV centers (Bernien et al., 2013).

To date, all experiments employing coherent photons from NV centers have been performed with NV centers that were formed during diamond growth. Key to their optical coherence is that these NV centers experience an environment with few defects, since the stability of optical transitions (as with many solid-state systems) suffers from unwanted interactions with nearby bulk and surface defects leading to changes in the strain and electric field environment (Manson et al., 2006; Fu et al., 2010; Orwa et al., 2011; Santori et al., 2010; Faraon et al., 2012). For NV centers with a broadened linewidth below $\approx 200$ MHz dominated by slow spectral diffusion, protocols using resonant charge repumping (Siyushev et al., 2013) and real-time monitoring of the transition frequency (Hensen et al., 2015) have been used to reduce the broadened linewidth to an effective linewidth of below $50$ MHz, suitable for quantum optical experiments. However, such protocols are challenging for NV centers with greater spectral diffusion.

Instead of being limited to NV centers formed during diamond growth, they can be created, for example by nitrogen ion implantation (Pezzagna et al., 2011). Nitrogen ion implantation provides an NV positioning accuracy that enables integration with on-chip photonics (Mouradian et al., 2015; Schröder et al., 2016) and coupling between nearby NV centers (Gaebel et al., 2006; Dolde et al., 2013; Yamamoto et al., 2013a). Precise positioning of NV centers or accurately registering their location is also a prerequisite for optimal overlap of the dipole with the electric field mode of diamond optical cavities, for engineering and enhancing light-matter interaction (Faraon et al., 2011, 2012; Hausmann et al., 2013; Lee et al., 2014; Li et al., 2015; Riedrich-Möller et al., 2015; Riedel et al., 2017). Moreover, ion implantation allows for the creation of single NV centers in high purity diamond, providing a potentially low-defect environment (Orwa et al., 2011).

However, the bombardment of the diamond with nitrogen ions creates crystal damage that can deteriorate spin and optical coherence properties of NV centers (Fu et al., 2010; Orwa et al., 2011). High-temperature annealing can mitigate some of these issues by repairing the diamond lattice (Lea-Wilson et al., 1995; Naydenov et al., 2010a; Yamamoto et al., 2013b; Deák et al., 2014). A procedure including a low implantation dose, careful cleaning, and high-temperature annealing was reported by Chu et al. (Chu et al., 2014), leading to the creation of narrow-linewidth NV centers. These narrow-linewidth NV centers can result from implanted nitrogen atoms, or from native nitrogen atoms, combined with for example implantation-induced vacancies (Figure 1a). In principle, the source of nitrogen can be verified by implanting 15N isotopes (natural abundance 0.37%) and resolving the hyperfine structure of the NV magnetic spectrum (Rabeau et al., 2006), as done in studies of the spin coherence (Ofori-Okai et al., 2012; Yamamoto et al., 2013b) and creation efficiency (Gaebel et al., 2006; Naydenov et al., 2010b; Toyli et al., 2010; Yamamoto et al., 2014; Becker et al., 2018) of NVs formed from implanted nitrogen. However, in Chu et al. (Chu et al., 2014) the isotope of the narrow-linewidth NV centers was not investigated (Chu, ). In a later study with similar results (Riedel et al., 2017), 14N isotopes were implanted, so that the origin of the NV center’s nitrogen atom could not be determined. Here we report on a study that enables us to directly correlate the optical linewidth of NV transitions to the NV formation mechanism.

To distinguish NVs formed by implanted nitrogen atoms from those formed by native nitrogen atoms, we implanted 15N isotopes (Rabeau et al., 2006). We then experimentally correlated the optical linewidth to the nitrogen isotope. The study was carried out on two separate samples sup . Sample A (processed at MIT) is a bulk $\left<100\right>$ CVD grown diamond (Element 6), prepared with the same implantation and annealing procedure as presented in Chu et al. (Chu et al., 2014): it was implanted with 15N+ at 85 keV with a fluence of $10^{9}$ N/cm2 and subsequently annealed at a maximum temperature of $1200$ *∘*C. Sample B (Delft) is a membrane (thickness $\approx 14$ µm) obtained from a bulk $\left<100\right>$ CVD grown diamond (Element 6), implanted with 15N+ at 400 keV (fluence $10^{8}$ N/cm2), and subsequently annealed at a maximum temperature of $1100$ *∘*C.

During implantation, nitrogen ions penetrate the diamond to a depth determined by the implantation energy (Figure 1). As implanted nitrogen atoms track through the crystal, they displace carbon atoms from their lattice sites creating vacancies. The nitrogen atoms create damage along the entire trajectory, but the damage is greatest near the stopping point (De Oliveira et al., 2017). We performed SRIM Ziegler et al. simulations to predict the stopping point of implanted 15N atoms, in addition to the locations of vacancies created along the trajectory (Figure 1b). At temperatures $>600$ *∘*C, vacancies become mobile (Davies et al., 1992). These vacancies can form an NV center, recombining with the implanted 15N that created the damage or with a native 14N in the lattice. The resulting 15NV and 14NV formation yields can vary significantly (Gaebel et al., 2006; Naydenov et al., 2010b; Toyli et al., 2010; Ofori-Okai et al., 2012; Yamamoto et al., 2014) depending on several factors, including the initial nitrogen concentration, the implantation fluence and energy, the number of vacancies created during the implantation process, and the duration and temperature of annealing.

A representative confocal fluorescence map at the implantation depth in sample A is shown in Figure 2a. Confocal fluorescence scans at foci deeper into the diamond show a significantly lower density of fluorescent spots (Figure 2a, inset), indicating that the emitters near the surface were predominantly created by the implantation and annealing process (sup, ). We identified emitters using different protocols in the two samples. In sample A, automated spot-recognition was performed on a fluorescence scan. For each detected spot we identified an NV center based on its characteristic zero-phonon line (ZPL) emission around 637 nm using a spectrograph from a photoluminescence measurement at 4 K under 532 nm excitation. This protocol identified 120 fluorescent spots as NV centers in a $\approx 400$ µm2 area. In sample B, spots in a fluorescence scan were detected visually, after which an automated protocol identified NV centers based on the presence of a resonance in an optically detected magnetic resonance (ODMR) spectrum around the characteristic NV center zero-field splitting of 2.88 GHz. In this way, 52 out of a total 57 inspected spots in a $\approx 75$ µm2 area in the implantation layer were identified as NV centers.

We next determined the nitrogen isotope of each NV center by observing the hyperfine structure of the ODMR spectra. A weak external magnetic field (B∥ $\approx$ 5-10 G) was applied to separate the $m_{s}=-1$ and $m_{s}=+1$ electron spin transitions. We found NV centers with the characteristic triplet splitting of the 14NV (with hyperfine splitting, $A=2.2$ MHz) as well as with the 15NV doublet ($A=3.1$ MHz) (Doherty et al., 2013), as indicated in Figure 2b. Of the 120 NVs identified on sample A, an ODMR signal was detected in 50, out of which 18 were 15NV, 18 14NV, and there were 14 in which the isotope could not be reliably determined from the ODMR spectra. Similarly, of the 52 NVs identified on sample B, 34 were 15NV, 3 were 14NV, and the isotope could not be determined in 15 NVs. We attribute the different isotope occurrence ratios in sample A and B to different native 14N content and different implantation fluence.

Subsequently, we measured the linewidth of optical transitions of identified NV centers, recording photoluminescence excitation (PLE) spectra at low temperature ($\approx 4$ K). A tunable laser with a wavelength near 637 nm was scanned over the optical transition while detecting emitted photons in the phonon-sideband. We performed two types of measurements. First, a scan was made in which resonant excitation (637 nm) and green illumination (532 nm) were rapidly interleaved at each data point. The red excitation causes rapid optical spin pumping and ionization of the NV center. The green excitation provides repumping into the negative charge state and the $m_{s}=0$ spin state. This measurement reveals the combined effect of short-time scale fluctuations and repump-laser-induced spectral diffusion in broadening the transition linewidth. Examples of the resulting traces are seen in Figure 2c.

Second, in sample B, an additional scan was performed to isolate the effect of short timescale fluctuations from repump-laser-induced diffusion. A single off-resonant repump was applied before sweeping the resonant laser at low power, as seen in Figure 2d. We applied microwaves on the spin resonances to prevent optical pumping into a dark spin state during the sweeps (Tamarat et al., 2008). Remaining traces in which the NV center ionized were excluded by applying a second scan over the resonance to check the charge state. If no resonance was observed, the preceding trace was disregarded. This scanning protocol was repeated many times to probe spectral diffusion through the resulting spread of the observed lines (Fu et al., 2009). To extract the linewidth free from repump-laser-induced spectral diffusion, we performed a weighted average of linewidth values found from Lorentzian fits to each individual scan.

Figures 2c and d display representative resonant optical scans for the 14NV and 15NV centers, each showing two resonances corresponding to the two $m_{s}=0$ orbital transitions $E_{x}$ and $E_{y}$. Notably, while the 14NV center (green, top row) exhibits a narrow optical linewidth with a full-width-at-half-maximum (FWHM) of $64\pm 4$ MHz, the 15NV linewidth (orange, bottom row) is broad, with a FWHM of $860\pm 236$ MHz. The dynamics in the second scan type (Figure 2d) indicate that both repump-induced fluctuations and a short-timescale mechanism broaden the 15NV linewidth, but that repump-induced fluctuations are dominant in broadening beyond 200 MHz (sup, ).

To correlate the occurrence of narrow optical linewidths with the N isotope of the NV centers, we acquired an extensive data set using the data accumulation procedures described above. The resulting distributions of optical linewidths for both N isotopes are shown in Figure 3. Narrow optical linewidths in both samples can be attributed almost exclusively to NVs with a native 14N host. In contrast, 15NV centers exhibiting narrow optical linewidths are extremely rare, with a median linewidth for 15NV centers of 3.1 GHz in sample A and 4.1 GHz in sample B.

Notably, in both datasets one NV center with a 15N host was found that showed narrow optical linewidths ($<100$ MHz). Given their low occurrence and the non-zero natural abundance of 15N, the creation mechanism of these narrow-linewidth 15NVs cannot be conclusively determined. Nevertheless, their presence demonstrates that 15NV centers can exhibit coherent optical transitions. Therefore, we conclude that the difference in distribution of optical linewidths between 14NVs and 15NVs is not due to an intrinsic effect related to the isotope itself, but due to differences in the local environment resulting from the implantation process.

Damage due to implantation may cause local strain fields. Axial strain results in an overall shift of the optical transition, while transverse strain will split the $E_{x}$ and $E_{y}$ transitions (Doherty et al., 2013). The distributions characterizing the strain for both NV isotopes are shown in Figure 4. The spread of the distribution in ZPL detuning representing axial strain for 15NVs (44 GHz for sample A, 60 GHz for sample B) is wider than for 14NVs (13 GHz for sample A, 5.6 GHz for sample B). Further, we found that 15NVs exhibit higher transverse strain, manifested by greater splitting with a median of 5.4 GHz (10 GHz) compared to 1.7 GHz (4.3 GHz) for 14NVs in sample A (B). Assuming a similar strain susceptibility for both isotopes, these results indicate that local damage around the implanted 15NVs creates a more strained environment, providing further evidence that implantation-induced local damage is responsible for the broadened 15NV linewidth. In addition, in both samples we observed a shift of the average ZPL frequency for 15NV compared to 14NV ZPLs, possibly due to an intrinsic dependency of the energy levels on the isotope as observed in other color centers (Dietrich et al., 2014; Ekimov et al., 2015).

The data show indications of an increase in 14NV density in the implantation layer in both samples (sup, ). We hypothesize that these 14NV centers can be formed from naturally occurring nitrogen combining with vacancies created during implantation. Since they can be at greater distance from the main damage center near the stopping point of the nitrogen, these NV centers may be coherent and useable for quantum information purposes; more work is needed for a statistically significant correlation. However, these NVs would have worse positioning accuracy as their spatial distribution is set by arbitrarily positioned naturally occurring nitrogen in combination with the diffusion length of the vacancies generated during implantation.

In summary, the implanted nitrogen atoms yield NV centers with predominantly broad optical lines ($>1$ GHz) and substantially higher strain than NV centers formed from native nitrogen. These results indicate that implanted nitrogen atoms combined with an annealing process at high temperatures do not routinely produce NV centers with narrow optical linewidths. Vacancies produced in the implantation process may combine with existing nitrogen atoms to produce narrow NVs, but more work is needed for a statistically significant correlation. It is clear from this work that recipes for generating implanted NV centers should be re-investigated, addressing local lattice damage associated with implanted nitrogen. In addition, other approaches for precisely controlling the NV centers’ positions while causing minimal local damage can be further explored, such as employing 2D nitrogen-doped diamond layers combined with electron irradiation or ion implantation for vacancy production (Ohno et al., 2012, 2014) or laser writing strategies for creating vacancies with 3D accuracy (Chen et al., 2017, 2018).