Statistically modeling optical linewidths of nitrogen vacancy centers in microstructures
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-08-27 |
| Journal | Physical review. B./Physical review. B |
| Authors | Mark Kasperczyk, Josh A. Zuber, Arne Barfuss, Johannes Kölbl, Viktoria Yurgens |
| Institutions | University of Basel |
| Citations | 17 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research investigates the relationship between nitrogen ion implantation techniques and the resulting optical linewidths of Nitrogen Vacancy (NV) centers in diamond microstructures, proposing a novel statistical framework for analysis.
- Core Finding on Linewidth Source: NV centers formed from native 14N nitrogen exhibit narrow linewidths (median ~100 MHz), confirming that native impurities are the primary source for spectrally stable qubits.
- Implantation Results: Implanted 15N generally yields broad linewidths (median ~3.5 GHz). However, a small, distinct population of implanted 15NV centers showed narrow linewidths (less than 500 MHz), suggesting implantation can occasionally yield high-quality centers.
- Novel Fabrication Method: The study introduces âpost-implantation,â where nitrogen is implanted after all nanofabrication (etching, structuring) is complete, aiming to mitigate fabrication-induced crystal damage.
- Structured Sample Performance: Post-implanted structured samples (as thin as 1.57 ”m) yielded NV centers with ZPL linewidths as narrow as less than 250 MHz, among the narrowest reported for standard etched structures.
- Statistical Modeling: A rigorous Bayesian statistical model, utilizing log-normal distributions, was developed to quantify parameter uncertainty, predict future linewidths, and enable quantitative comparison of results across different research groups and fabrication recipes.
- Strain Independence: Linewidth distribution was found to be independent of the NV centerâs location (bulk vs. structured) and largely uncorrelated with ZPL wavelength (local strain environment).
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Purity (N) | < 5 | ppb | Electronic grade starting material |
| Diamond Purity (B) | < 1 | ppb | Electronic grade starting material |
| Transform Limited Linewidth | ~13 | MHz | Theoretical minimum optical linewidth |
| Acceptable Linewidth (Microcavity) | 100 | MHz | Requirement for decent microcavity coupling [4] |
| Sample A Implantation Isotope | 14N | N/A | Implanted nitrogen isotope |
| Sample B Implantation Isotope | 15N | N/A | Implanted nitrogen isotope |
| Implantation Energy (Samples A & B) | 12 | keV | Ion implantation energy |
| Implantation Fluence (Samples A & B) | 1011 | ions/cm2 | Ion dose |
| Implantation Angle | 7 | ° | Angle relative to sample mount |
| Membrane Thickness Range | 2.5 - 5 | ”m | Non-uniform structured area |
| Cantilever Thickness Range | 2.5 - 4 | ”m | Structured area |
| Narrowest Linewidth (Structured, Sample C) | < 250 | MHz | Observed in 1.57 ”m thick area (post-implanted) |
| Median Linewidth (Native 14NV, Sample B) | ~100 | MHz | Narrow population, isotopically classified |
| Median Linewidth (Implanted 15NV, Sample B) | ~3.5 | GHz | Broad population, isotopically classified |
| Natural Abundance of 15N | 0.37 | % | Used for distinguishing native vs. implanted N |
Key Methodologies
Section titled âKey MethodologiesâThe study employed a multi-step fabrication and characterization process, focusing on the novel post-implantation approach:
- Material Preparation: Electronic grade diamond (N < 5 ppb, B < 1 ppb) was used as the substrate.
- Nanofabrication: Membranes and cantilevers were fabricated using established etching procedures [23]. Dimensions included membranes (2.5-5 ”m thick) and cantilevers (2.5-4 ”m thick).
- Post-Implantation: Nitrogen ions (14N or 15N) were implanted after all structuring was completed.
- Sample A (14N): 12 keV energy, 1011 ions/cm2 fluence, 7° angle.
- Sample B (15N): 12 keV energy, 1011 ions/cm2 fluence, 7° angle.
- Sample C (15N): 52 keV energy, 5 x 109 ions/cm2 fluence, 7° angle.
- Annealing Cycle: Samples were annealed in three stages to repair lattice damage and form NV centers: 4 hours at 400 °C, 10 hours at 800 °C, and 2 hours at 1200 °C.
- Cleaning: A tri-acid clean was performed post-annealing.
- Optical Characterization:
- Confocal fluorescence mapping (532 nm excitation) was used to locate potential NV centers.
- Photoluminescence Excitation (PLE) spectroscopy (637 nm sweep) measured the excited state transition linewidth (ZPL). Linewidths were extracted using a Gaussian fit, accounting for spectral diffusion.
- Isotopic Classification: Pulsed Optically Detected Magnetic Resonance (ODMR) was used to measure the hyperfine structure, allowing classification of NV centers as 14NV (native) or 15NV (implanted).
- Statistical Modeling: A Bayesian approach was implemented using a log-normal likelihood distribution to model the linewidth data, providing Maximum A Posteriori (MAP) estimates and credible intervals for the median (”) and standard deviation (Ï) of the linewidth populations.
Commercial Applications
Section titled âCommercial ApplicationsâThis research directly supports the engineering and optimization of quantum devices based on diamond NV centers, particularly where high spectral stability is paramount.
- Quantum Computing and Entanglement: Provides a methodology for reliably creating spectrally narrow NV centers necessary for high-fidelity entanglement protocols and scalable quantum architectures.
- Integrated Quantum Photonics: The ability to achieve narrow linewidths (< 250 MHz) in thin, structured diamond membranes is critical for efficient coupling of NV centers to photonic cavities and waveguides.
- High-Coherence Quantum Sensing: Optimizing NV formation to minimize spectral diffusion and inhomogeneous broadening enhances the sensitivity and coherence time of NV-based magnetometers, electrometers, and thermometers.
- Advanced Diamond Material Processing: The statistical model offers a quantitative tool for comparing and validating different diamond fabrication recipes (e.g., implantation energy, annealing cycles, etching techniques) to maximize the yield of high-quality qubits.
- Isotope Engineering: Confirms the importance of using isotopically pure diamond or highly controlled implantation to manage the source of nitrogen, which dictates the final spectral quality of the NV center population.
View Original Abstract
We investigate the effects of a novel approach to diamond nanofabrication and nitrogen vacancy (NV) center formation on the optical linewidth of the NV zero-phonon line (ZPL). In this post-implantation method, nitrogen is implanted after all fabrication processes have been completed. We examine three post-implanted samples, one implanted with $^{14}$N and two with $^{15}$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 occuring 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 $^{15}$NV centers with narrow ($<500,\mathrm{MHz}$) 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.