Indirect Control of the $rm {}^{29}SiV^{-}$ Nuclear Spin in Diamond
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-03-19 |
| Journal | arXiv (Cornell University) |
| Authors | Hyma H. Vallabhapurapu, Chris Adambukulam, André Saraiva, Arne Laucht |
| Analysis | Full AI Review Included |
Technical Documentation and Analysis: High-Speed Nuclear Spin Control in 29SiV- Diamond
Section titled âTechnical Documentation and Analysis: High-Speed Nuclear Spin Control in 29SiV- DiamondâExecutive Summary
Section titled âExecutive SummaryâThis research demonstrates a powerful simulation pathway for achieving fast, coherent control of the 29SiV- host nuclear spin in diamond, significantly accelerating quantum gate operations compared to conventional methods.
- Core Achievement: Simulation and optimization of single-qubit nuclear spin gates (X, Y, Z, H, S, T) using indirect control (IC) via instantaneous electron $\pi$-rotations in the Silicon-Vacancy (SiV-) defect.
- Performance: Achieved high simulated gate fidelities (F ≥ 0.98), with the fastest gate times on the order of hundreds of nanoseconds (209.06 ns for the unstrained X gate).
- Methodological Breakthrough: The large spin-orbit coupling (ASO = 46 GHz) inherent in the SiV- Hamiltonian replaces the need for appreciable hyperfine anisotropy, simplifying requirements for indirect control.
- Control Mechanism: The IC gate sequence relies on rapid electron $\pi$-rotations and specific free precession delays (Ï1-Ï4) to manipulate the nuclear spin orientation angle (ÎΞ).
- Material Requirements: The technique relies fundamentally on high-quality single crystal diamond hosting stable SiV- centers, necessitating substrates amenable to precise strain engineering or high-purity, naturally unstrained growth.
- Future Vision: The approach is compatible with all-optical control techniques using picosecond $\pi$-rotations, enabling integration into scalable nanophotonic quantum registers.
Technical Specifications
Section titled âTechnical SpecificationsâThe following table summarizes the key physical constants and performance parameters extracted from the simulation and Hamiltonian analysis.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Target Qubit System | 29SiV- | Defect | Silicon Vacancy in Diamond |
| Isotopic Qubit | 29Si | I=1/2 | Host nuclear spin used for quantum memory |
| Electron Gyromagnetic Ratio ($\gamma$e) | 28 | GHz/T | Used in Hamiltonian definition |
| Nuclear Gyromagnetic Ratio ($\gamma$n) | -8.46 | MHz/T | Used in Hamiltonian definition |
| Spin-Orbit Coupling (ASO) | 46 | GHz | Ground state coupling parameter |
| Hyperfine Coupling (Aâ„) | 78 | MHz | Hyperfine $\perp$ SiV--axis |
| Required Magnetic Field Angle (Bo) | 54.7 | ° | Relative to SiV- symmetry axis ([111] axis) |
| Simulated Gate Fidelity (Average, F) | ≥ 0.98 | N/A | Across X, Y, Z, H, S, T gates |
| Fastest Gate Time (X, Unstrained Case âAâ) | 209.06 | ns | High-speed, megahertz rate operation |
| Slowest Gate Time (X, Strained Case âBâ) | 1296.50 | ns | Limited by lower nuclear spin precession frequencies |
| Strain Regimes Investigated | 0 and 150 | GHz | Unstrained and moderately strained cases |
Detailed Gate Time Performance (Unstrained Case âAâ vs. Strained Case âBâ)
| Gate | Strain Case | $\tau$1 (ns) | $\tau$2 (ns) | $\tau$3 (ns) | $\tau$4 (ns) | Total Time (ns) | Fidelity (F) |
|---|---|---|---|---|---|---|---|
| X | Unstrained (A) | 2.99 | 172.96 | 22.66 | 10.46 | 209.06 | ≥0.99 |
| X | Strained (B) | 245.39 | 1.49 | 401.84 | 647.73 | 1296.50 | ≥0.99 |
| Y | Unstrained (A) | 11.73 | 197.03 | 84.09 | 20.73 | 313.59 | ≥0.99 |
| H | Unstrained (A) | 29.33 | 111.23 | 10.55 | 5.69 | 156.79 | ≥0.99 |
| H | Strained (B) | 28.76 | 162.03 | 196.84 | 260.61 | 648.23 | ≥0.98 |
| T | Unstrained (A) | 4.49 | 88.29 | 34.56 | 29.47 | 156.79 | ≥0.99 |
Key Methodologies
Section titled âKey MethodologiesâThe indirect control (IC) mechanism for the 29SiV- nuclear spin involves precise, time-optimized sequences of electron $\pi$-rotations separated by free precession delays ($\tau$).
- Hamiltonian Definition: The total system is modeled using the 29SiV- Hamiltonian, incorporating electron/nuclear Zeeman terms (He, Hn), Hyperfine coupling (Hhf), Spin-Orbit coupling (HSO, 46 GHz), and Strain (Hstr).
- Strain Regime Selection: Simulations investigate both the unstrained ($\alpha=\beta=0$ GHz) and strained ($\alpha=\beta=150$ GHz) regimes, chosen to mix orbitals sufficiently to allow electron spin transitions.
- Magnetic Field Alignment (Bo): An external static magnetic field (Bo) is applied at a specific non-zero, non-parallel angle (54.7° away from the SiV axis) to ensure the nuclear spin quantization axes change upon electron spin flip.
- Indirect Control Gate Sequence: Gates (X, Y, Z, H, S, T) are constructed using a series of instantaneous electron $\pi$-rotations ($\pi$1, $\pi$2, $\pi$3, $\pi$4) separated by four optimized free precession delays ($\tau$1, $\tau$2, $\tau$3, $\tau$4).
- Numerical Optimization: Matlabâs âSurrogate Optimizationâ solver is used to minimize the total gate time (Tgate) while maximizing the overlap (|<$\tau$|$\phi$opt>|2) between the systemâs final time-evolved state ($\phi$opt) and the deterministic target state ($\tau$), ensuring high fidelity (F $\ge$ 0.98).
- Phase Correction: A padding delay ($\tau$4) is added to the end of the sequence to ensure the rotating frame of the nuclear spin returns to phase with the lab frame, guaranteeing consistency for complex gate operations.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe research highlights the critical need for high-purity, minimally strained diamond substrates capable of hosting stable quantum defects and undergoing advanced post-processing like strain engineering. 6CCVD is uniquely positioned to supply the foundational materials necessary to replicate and advance this SiV- quantum control research.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate the high-fidelity results demonstrated in this paper, researchers require diamond substrates optimized for quantum defect stability and optical integration.
- Optical Grade SCD (Single Crystal Diamond): Required for achieving the lowest native strain (to emulate the âunstrainedâ regime) and maintaining the long coherence times essential for nuclear spin quantum memory.
- Recommendation: High-ppurity, low-nitrogen MPCVD SCD plates, specifically grown or cut to precise crystallographic orientations (e.g., [100] as mentioned in the paper, or [111]).
- Isotopically Purified Diamond: While 29Si is the active qubit, minimizing other nuclear spin bath interactions (e.g., 13C) is crucial for extending coherence times.
- Recommendation: Supply of SCD grown using tailored isotopic gases, such as enriched 12C diamond (Purity > 99.999%), providing a superior, low-noise environment for the 29SiV- qubit.
Customization Potential for Quantum Devices
Section titled âCustomization Potential for Quantum DevicesâThe realization of the âstrainedâ regime and integration of high-speed optical control components rely heavily on custom fabrication capabilities.
| 6CCVD Service | Benefit to 29SiV- Research | Technical Capability |
|---|---|---|
| Custom Dimensions & Orientation | Provides samples necessary for precise magnetic field alignment (54.7°) and integration into cryogenic/microscopy setups. | Plates/wafers up to 125mm (PCD) and custom laser cutting services. |
| Ultra-Low Roughness Polishing | Essential for implementing all-optical control and reducing surface decoherence effects on the SiV- optical transition. | SCD Polishing: Ra < 1nm; Inch-size PCD Polishing: Ra < 5nm. |
| Integrated Metalization | Allows prototyping of on-chip RF/MW antennas or electrodes required for hybrid (optical + MW) control protocols, even if purely optical is sought. | Custom deposition of Au, Pt, Pd, Ti, W, Cu layers. |
| Controlled Thickness | Enables wafer bonding or integration with photonic structures (e.g., photonic crystal cavities mentioned in related literature [9, 22]). | Thickness control for SCD/PCD from 0.1 ”m up to 500 ”m. |
Engineering Support
Section titled âEngineering SupportâThis research demonstrates that optimal quantum control requires intricate material selection, precise crystallographic alignment, and careful strain management.
6CCVDâs in-house PhD team can assist researchers in material selection, determining the appropriate SCD purity and thickness required to manage internal strain levels, facilitating projects focused on SiV-based quantum computing and sensing. We provide detailed material characterization data to ensure substrates meet the exacting requirements for ultra-low temperature, high-fidelity quantum experiments.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Coherent control and optical readout of the electron spin of the $^{29}$SiV$^{-}$ center in diamond has been demonstrated in literature, with exciting prospects for implementations as memory nodes and spin qubits. Nuclear spins may be even better suited for many applications in quantum information processing due to their long coherence times. Control of the $^{29}$SiV$^{-}$ nuclear spin using conventional NMR techniques is feasible, albeit at slow kilohertz rates due to the nuclear spinâs low gyromagnetic ratio. In this work we theoretically demonstrate how indirect control using the electron spin-orbit effect can be employed for high-speed, megahertz control of the $^{29}$Si nuclear spin. We discuss the impact of the nuclear spin precession frequency on gate times and the exciting possibility of all optical nuclear spin control.