Effect of intersystem crossing rates and optical illumination on the polarization of nuclear spins close to nitrogen-vacancy centers
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-05-27 |
| Journal | Physical review. B./Physical review. B |
| Authors | H. Duarte, Hossein T. Dinani, V. Jacques, J. R. Maze |
| Institutions | Centre National de la Recherche Scientifique, Universidad Mayor |
| Citations | 6 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Optimizing Nuclear Spin Polarization in NV Centers
Section titled âTechnical Documentation & Analysis: Optimizing Nuclear Spin Polarization in NV CentersâThis document analyzes the research paper âEffect of inter-system crossing rates and optical illumination on the polarization of nuclear spins nearby nitrogen-vacancy centersâ to provide technical specifications and highlight how 6CCVDâs advanced MPCVD diamond materials and fabrication services directly support and enable this critical quantum research.
Executive Summary
Section titled âExecutive SummaryâThe research investigates the fundamental dynamics governing nuclear spin polarization near Nitrogen-Vacancy (NV) centers in diamond, a crucial step for quantum information processing and metrology.
- Core Achievement: Demonstrated that nuclear spin polarization efficiency is highly sensitive to the specific transition rates involved in the NV centerâs electronic inter-system crossing (ISC).
- Optimal Performance: Achieved high nuclear spin polarization (up to $\approx 95%$ for ${}^{15}\text{N}$) using the Excited State Level Anti-Crossing (ESLAC) method, validating Model 4 of the ISC rates.
- Material Requirement: The success of these methods relies entirely on high-purity diamond substrates capable of supporting long electronic and nuclear coherence times ($T_{1,el} \approx 1\text{ ms}$, $T_{1,n} \approx 100\text{ ms}$).
- Methodology: Compared three polarization techniques: ESLAC, and nuclear spin precession while the electronic spin is in the $m_s = 0$ and $m_s = 1$ states, analyzing performance based on optical excitation power ($k$).
- 6CCVD Value Proposition: 6CCVD provides the necessary foundationâultra-high purity Single Crystal Diamond (SCD) with custom isotopic control and advanced surface preparationârequired to replicate and extend these high-coherence quantum experiments.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the analysis of the NV center dynamics and polarization methods:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Maximum Nuclear Polarization | $\approx 95$ | % | ${}^{15}\text{N}$ using ESLAC (Model 4) |
| Optical Excitation Rate ($k$) Range | 4 to 70 | MHz | Range tested for polarization dependence |
| ESLAC Magnetic Field ($B_z$) | $\approx 510$ | G | Optimal field for Excited State Level Anti-Crossing |
| Spontaneous Decay Rate ($\gamma$) | 62.7 to 77 | MHz | Range across Models 1-4 |
| ISC Rate ($k_{+,s}$) | 30 to 91.6 | MHz | Excited $m_s=+1$ to Singlet (Model dependent) |
| ISC Rate ($k_{s,0}$) | 3.3 to 4.83 | MHz | Singlet to Ground $m_s=0$ (Model dependent) |
| Electron Spin $T_{2,el}$ (Ground) | 3 | ”s | Coherence time used in simulation |
| Electron Spin $T_{1,el}$ | 1 | ms | Relaxation time used in simulation |
| Nuclear Spin $T_{1,n}$ | 100 | ms | Relaxation time used in simulation |
| Required $B_z$ for $m_s=1$ Precession | $\approx 1000$ | G | Required for far ${}^{13}\text{C}$ spins (Family J) |
Key Methodologies
Section titled âKey MethodologiesâThe research utilized a seven-level model of the NV center electronic spin combined with the Markovian master equation to simulate density matrix evolution.
- Material System: NV centers in diamond, focusing on nearby ${}^{13}\text{C}$ and ${}^{15}\text{N}$ nuclear spins.
- Electronic Spin Modeling: Four distinct transition rate models (Models 1-4) were used to describe the inter-system crossing (ISC) rates between the triplet ground/excited states and the metastable singlet states.
- Optical Excitation: Continuous wave optical illumination was modeled with variable excitation rates ($k$) to analyze power dependence on polarization efficiency.
- Polarization Method 1: ESLAC:
- Applied a magnetic field ($B_z \approx 510\text{ G}$) along the NV axis.
- Relies on the perpendicular component of the hyperfine interaction ($A_{\perp}$) to cause electron-nuclear spin flip-flops in the excited state.
- Polarization Method 2: Nuclear Spin Precession on $m_s = 0$:
- Involves optical pumping, a selective microwave (MW) pulse, and nuclear spin precession driven by an external perpendicular magnetic field ($B_x$).
- Polarization Method 3: Nuclear Spin Precession on $m_s = 1$:
- Requires a large magnetic field ($B_z = -A_{zz}/\gamma_n$) along the NV axis to bring ground states $|1, \uparrow\rangle$ and $|1, \downarrow\rangle$ close.
- Precession is driven by the anisotropic component of the hyperfine interaction ($A_{ani}$).
- Performance Metric: Nuclear polarization ($P_n$) was calculated as the difference in population between the nuclear spin projections: $P_n = |\rho_n(\uparrow, \uparrow) - \rho_n(\downarrow, \downarrow)|$.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research underscores the critical need for ultra-high quality diamond substrates to maintain the long coherence times ($T_{1,n} \approx 100\text{ ms}$) necessary for high-fidelity nuclear spin polarization. 6CCVD is uniquely positioned to supply the foundational materials and custom fabrication required to advance this quantum technology.
| Research Requirement | 6CCVD Solution & Capability | Technical Advantage |
|---|---|---|
| High Coherence Substrates | Optical Grade Single Crystal Diamond (SCD) | Ultra-low nitrogen concentration (P1 centers) ensures minimal electronic spin decoherence, maximizing $T_{1,el}$ and $T_{2,el}$ for robust NV center operation. |
| Isotopic Control | Isotopically Controlled SCD | We supply ${}^{12}\text{C}$ enriched diamond to suppress background nuclear spin noise, extending the critical nuclear coherence time ($T_{2,n}$) far beyond the $1\text{ ms}$ used in these simulations. |
| Custom Dimensions | Plates/Wafers up to 125 mm (PCD) | Provides large-area substrates for scaling up quantum devices and integrating complex microwave circuitry. SCD available up to $500\text{ ”m}$ thickness. |
| Microwave Control Integration | Custom Metalization Services | The precession methods require precise MW delivery. 6CCVD offers in-house deposition of Au, Pt, Ti, W, and Cu for fabricating high-performance microwave strip lines and antennas directly onto the diamond surface. |
| Surface Quality | Precision Polishing (Ra < 1 nm SCD) | Ultra-smooth surfaces are essential for minimizing optical scattering losses and ensuring high-fidelity optical excitation and readout, critical for the ESLAC method. |
| Advanced Doping/Implantation | Custom Substrates for ${}^{15}\text{N}$ NV Creation | We provide substrates optimized for controlled ion implantation or in-situ doping, enabling researchers to precisely control the concentration and depth of ${}^{15}\text{N}$ NV centers required for high-efficiency polarization. |
Engineering Support
Section titled âEngineering SupportâThe complex dependence of nuclear polarization on ISC rates and magnetic field alignment (as shown in Figure 6) necessitates precise material selection. 6CCVDâs in-house PhD team specializes in MPCVD growth parameters and defect engineering, offering expert consultation to assist researchers in selecting the optimal diamond specifications (purity, isotopic enrichment, and surface termination) for similar NV-based Quantum Metrology and Information Processing projects.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Several efforts have been made to polarize the nearby nuclear environment of nitrogen vacancy (NV) centers for quantum metrology and quantum information applications. Different methods showed different nuclear spin polarization efficiencies and rely on electronic spin polarization associated to the NV center, which in turn crucially depends on the inter-system crossing. Recently, the rates involved in the inter-system crossing have been measured leading to different transition rate models. Here, we consider the effect of these rates on several nuclear polarization methods based on the level anti-crossing, and precession of the nuclear population while the electronic spin is in the ms = 0 and ms = 1 spin states. We show that the nuclear polarization depends on the power of optical excitation used to polarize the electronic spin. The degree of nuclear spin polarization is different for each transition rate model. Therefore, the results presented here are relevant for validating these models and for polarizing nuclear spins. Furthermore, we analyze the performance of each method by considering the nuclear position relative to the symmetry axis of the NV center.