Longitudinal spin relaxation model applied to point-defect qubit systems
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-04-17 |
| Journal | Physical review. B./Physical review. B |
| Authors | Viktor IvĂĄdy |
| Institutions | Linköping University, HUN-REN Wigner Research Centre for Physics |
| Citations | 27 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research presents a robust theoretical framework for simulating longitudinal spin relaxation (T1) in solid-state point defect qubits, crucial for quantum technology applications.
- Core Methodology: An extended Lindblad equation formalism is developed, utilizing a cluster approximation (CA) to model the dynamics of a central spin (e.g., NV center) interacting with a complex, dilute spin bath.
- Accurate T1 Prediction: The method accurately calculates the T1 relaxation time of the NV center in diamond across a wide range of external magnetic fields and strain conditions.
- Spin Bath Modeling: The model successfully incorporates multiple environmental spin species, including P1 centers, environmental NV centers, and 13C nuclear spins, capturing all known characteristics of their relaxation patterns.
- Validation of Approximation: Numerical results validate the use of the non-entangled spin bath approximation (T2bath << 1/|h0i|) for P1 and NV environments, enabling quantitative results comparable to experimental data.
- Enhanced Relaxation Peaks: Simulations identify specific magnetic field values (e.g., 51 mT and 102 mT for P1 bath) where enhanced spin flip-flop rates occur due to level crossings, providing critical design parameters for quantum devices.
- Strain Dependence: The model demonstrates how applied parallel and perpendicular strain can significantly alter relaxation rates by opening small energy gaps between degenerate states, offering a control mechanism for qubit stability.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Central Spin Zero Field Splitting (D) | 2.870 | GHz | NV center in diamond |
| P1 Center 14N Quadrupole Splitting (P) | 5.01 | MHz | Used in P1 center Hamiltonian |
| P1 Center 14N Hyperfine Tensor (Azz) | 114 | MHz | Calculated via DFT |
| P1 Center 14N Hyperfine Tensor (Axx, Ayy) | 81 | MHz | Calculated via DFT |
| Magnetic Field Range (Investigated) | 0 to 102 | mT | Range of T1 dependence study |
| P1 Center Concentration (Sample S2) | 50 | ppm | Used for P1 bath simulations |
| Environmental NV Concentration | 8, 12 | ppm | Used for NV bath simulations |
| 13C Nuclear Spin Abundance | 1.07 | % | Natural abundance used for simulation |
| Typical Simulated T1 Time (P1 bath) | > 1 | ms | Validates non-entangled bath approximation |
| DFT Supercell Size | 1728 | atoms | Electronic structure calculation |
| DFT Functional | HSE06 | N/A | Hybrid functional used for electronic structure |
| DFT Plane Wave Basis Set Cutoff | 420 | eV | VASP implementation detail |
Key Methodologies
Section titled âKey MethodologiesâThe simulation relies on a self-consistent, time-dependent propagation cycle within an extended quantum formalism:
- Hamiltonian Definition: The system Hamiltonian (H0) is defined non-approximately, including the central spin (s0), environmental spins (si), and their pairwise coupling terms (h0i).
- Cluster Approximation (CA): The many-spin system is broken down into overlapping clusters (CN).
- First Order (C1): Each cluster contains the central spin (s0) and only one environmental spin (si). This is the primary approximation used, neglecting entanglement within the spin bath.
- Mean Intra-Spin Bath Field (Effective Field):
- An effective field (alpha, beta) is calculated semi-classically from the polarization of the environmental spins. This field shifts the central spin energy levels (Overhauser field effect) but preserves the diagonal elements of the density matrix.
- Extended Lindbladian (L): Time-dependent Lindbladian terms are introduced to the master equations of the clusters (Lc0, Lci).
- These terms enforce a non-unitary coupling between clusters, ensuring that the diagonal elements (populations) of the central spinâs reduced density matrix are identical across all clusters at any time t.
- Self-Consistent Rate Determination: Time-dependent flip-flop rates (b0l, bil) are calculated based on the additivity of the difference in intrinsic flip-flop rates (Delta-alpha) between the reference cluster (c0) and the coupled clusters (ci).
- Time Propagation: The cluster density matrices are propagated over infinitesimal time steps (dt) using the Runge-Kutta method, iteratively updating the effective fields and flip-flop rates.
- First Principles Parameterization: Density Functional Theory (DFT) calculations (using HSE06 functional, 1728-atom supercell) were performed to obtain accurate hyperfine coupling tensors required for the NV-13C and NV-P1 spin interactions.
Commercial Applications
Section titled âCommercial ApplicationsâThe ability to accurately model spin relaxation dynamics (T1) is critical for optimizing the performance and lifetime of solid-state quantum devices.
- Quantum Sensing and Metrology:
- Application: Designing NV-based magnetometers, electrometers, and thermometers. T1 determines the maximum integration time and sensitivity of continuous-wave sensing protocols.
- Value: Enables predictive modeling of sensor performance under operational strain and magnetic bias fields, reducing the need for extensive empirical testing.
- Quantum Computing and Information:
- Application: Developing robust solid-state qubits (e.g., NV electron spin coupled to nuclear spins).
- Value: Provides a quantitative understanding of decoherence mechanisms, allowing engineers to select optimal defect concentrations and external control parameters to maximize qubit lifetime and fidelity.
- Materials Science and Defect Engineering:
- Application: Guiding the synthesis and processing of diamond and other wide bandgap semiconductors (e.g., SiC) to control the concentration and orientation of spin defects (P1, NV).
- Value: Allows for targeted material growth specifications (e.g., maximum acceptable P1 concentration) to meet specific T1 requirements for commercial quantum hardware.
- Dynamic Nuclear Polarization (DNP):
- Application: Optimizing spin polarization transfer from NV centers to bulk nuclear spins for hyperpolarization, used to enhance signal-to-noise ratio in NMR/MRI.
- Value: The model accurately simulates the conditions (magnetic field and coupling strength) required for efficient spin polarization transfer.
View Original Abstract
Controllable, partially isolated few level systems in semiconductors have\nrecently gained multidisciplinary attention due to their widespread nanoscale\nsensing and quantum technology applications. Quantitative simulation of the\ndynamics and related applications of such systems is a challenging theoretical\ntask that requires faithful description not only the few level systems but also\ntheir local environments. Here, we develop a method that can describe relevant\nrelaxation processes induced by a dilute bath of nuclear and electron spins.\nThe method utilizes an extended Lindblad equation in the framework of cluster\napproximation of a central spin system. We demonstrate that the proposed method\ncan accurately describe T$_1$ time of an exemplary solid-state point defect\nqubit system, in particular NV center in diamond, at various magnetic fields\nand strain.\n