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, Federico Santa MarĂa Technical University |
| Citations | 6 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive Summaryâ- Core Objective: The study investigates how four different models of Nitrogen-Vacancy (NV) center electronic spin dynamics (Inter-System Crossing, ISC) affect the efficiency of nearby nuclear spin polarization (NSP).
- Key Dependence: NSP efficiency is shown to depend critically on the optical excitation rate ($k$) used to polarize the electronic spin, as this rate influences the population distribution across the singlet and ground states.
- ESLAC Performance: The Excited State Level Anti-Crossing (ESLAC) method achieved the highest simulated NSP (up to 95% for 15N) using Model 4 ISC rates, which aligns best with existing experimental data.
- Precession Method Sensitivity: Nuclear precession methods (ms = 0 and ms = 1) are highly sensitive to the electronic spin polarization achieved during the initial optical pumping phase, making them more susceptible to variations in ISC rates and optical power.
- Model Comparison: Model 1 (an older ISC model) yields higher NSP at large optical excitation rates for the ms = 0 precession method, whereas Models 2-4 show decreasing NSP with increasing $k$.
- Method Selection by Position: ESLAC and ms = 0 precession are suitable for polarizing nuclear spins close to the NV center. The ms = 1 precession method is more practical for far nuclear spins (e.g., 13C families requiring magnetic fields less than 1000 G).
- Validation Tool: The results provide a framework for using nuclear spins as a sensitive measuring tool to experimentally validate and distinguish between competing ISC transition rate models.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Ground State ZFS ($D_g$) | 2.87 | GHz | Zero Field Splitting (ZFS) between ms = 0 and ms = ±1. |
| Excited State ZFS ($D_e$) | 1.42 | GHz | ZFS between ms = 0 and ms = ±1. |
| Electronic Gyromagnetic Ratio ($\gamma$el) | 2.8 | MHz/G | Standard value for NV electronic spin. |
| 13C Nuclear Gyromagnetic Ratio ($\gamma$n) | 1.07 | kHz/G | Standard value for 13C nuclear spin. |
| ESLAC Magnetic Field ($B_z$) | ~510 | G | External field applied along the NV axis. |
| ESLAC 15N NSP (Model 4) | ~95 | % | Highest simulated nuclear spin polarization achieved. |
| Spontaneous Decay Rate ($\gamma$) | 62.7 to 77 | MHz | Range of rates used across Models 1-4. |
| Optical Excitation Rate ($k$) Range | 10 to 70 | MHz | Range tested for polarization dependence. |
| Singlet State Lifetime (Relative) | ~30 | Times Slower | Singlet population relaxes to ground state 30 times slower than spontaneous decay ($\gamma$). |
| NV Electron Spin T2,el (Ground State) | 3 | ”s | Transverse relaxation time used in simulations. |
| NV Electron Spin T1,el | 1 | ms | Longitudinal relaxation time used in simulations. |
| 15N Quadrupole Interaction ($Q$) | -4.96 | MHz | Additional term in Hamiltonian for 14N (spin 1). |
Key Methodologies
Section titled âKey Methodologiesâ- NV Center Modeling: A seven-level model was employed for the NV electronic spin, incorporating the ground state (3A2), excited state (3E), and metastable singlet states (S).
- ISC Rate Comparison: Four distinct sets of Inter-System Crossing (ISC) transition rates (Models 1, 2, 3, and 4) were implemented to simulate the spin-dependent transitions between triplet and singlet states.
- Master Equation Simulation: The dynamics of the combined electron-nuclear spin density matrix were calculated using the Markovian master equation (Lindbladian formalism), assuming room temperature conditions.
- ESLAC Protocol: Polarization is achieved by applying a large magnetic field ($B_z \approx 510$ G) along the NV axis. Optical excitation drives the electron, and the perpendicular hyperfine component ($A_{\perp}$) causes flip-flops between electron and nuclear spins in the excited state.
- ms = 0 Precession Protocol: The electron spin is first polarized to ms = 0 via optical pumping. A selective microwave pulse transfers population, allowing the nuclear spin to precess in the ms = 0 state due to a perpendicular magnetic field component ($B_{\perp}$).
- ms = 1 Precession Protocol: This method requires setting the magnetic field along the NV axis such that $B_z = -A_{zz}/\gamma_n$. Polarization relies on the anisotropic hyperfine component ($A_{ani}$) causing nuclear spin precession while the electron is in the ms = 1 state.
- Hyperfine Interaction Analysis: The Hamiltonian included the hyperfine interaction ($H_{i,hf}$), analyzed primarily using the secular approximation (terms proportional to $S_z$). Non-secular terms were included perturbatively using a second-order correction term ($H_{soc}$) to improve accuracy.
Commercial Applications
Section titled âCommercial Applicationsâ- Quantum Computing and Memory: High-fidelity initialization and readout of nuclear spins (e.g., 13C, 15N) are essential for utilizing them as long-coherence qubits for quantum information storage and processing.
- Nanoscale Magnetic Resonance Imaging (MRI): Enhanced nuclear spin polarization increases the signal-to-noise ratio in NV-based NMR and MRI, enabling high-resolution chemical analysis and sensing at the single-molecule level.
- Quantum Sensing and Metrology: The ability to efficiently polarize nuclear spins enhances the coherence time of the NV electronic spin, improving the sensitivity of NV magnetometers and thermometers.
- Diamond Material Science: The results inform the engineering of NV centers in diamond films (e.g., via CVD processes) by linking fundamental electronic dynamics (ISC rates) to practical device performance (polarization efficiency).
- Hyperpolarization Technology: The methods can be adapted for hyperpolarizing bulk diamond powder or external molecules on the diamond surface, which is valuable for medical diagnostics and advanced materials research.
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.