Indirect Control of the $rm {}^{29}SiV^{-}$ Nuclear Spin in Diamond
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2022-03-19 |
| Journal | arXiv (Cornell University) |
| Authors | Hyma H. Vallabhapurapu, Chris Adambukulam, AndrƩ Saraiva, Arne Laucht |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive SummaryāThis analysis summarizes a theoretical demonstration of high-speed, coherent control over the host 29Si nuclear spin within the Silicon Vacancy (SiV-) center in diamond, utilizing an Indirect Control (IC) technique.
- Core Value Proposition: Achieves megahertz (MHz) rate control of the 29Si nuclear spin, resulting in gate durations in the hundreds of nanoseconds. This is significantly faster than conventional Nuclear Magnetic Resonance (NMR) techniques, which are limited to kilohertz (kHz) rates due to the low nuclear gyromagnetic ratio.
- Mechanism: Indirect Control (IC) leverages the large electron spin-orbit coupling (ASO ā 46 GHz) inherent to the SiV- center. This coupling creates an anisotropic effective magnetic field (Bnet) on the nuclear spin when the electron spin state is flipped.
- Quantization Axis Change (ĪĪø): The spin-orbit effect replaces the need for explicit hyperfine anisotropy, enabling a large change in the nuclear spin quantization direction (ĪĪø up to 90Ā° or 120Ā°) necessary for two-axis control.
- Gate Performance: Simulated single-qubit gates (X, Y, Z, H, S, T) were demonstrated with high average fidelity (F ā„ 0.98) in both unstrained (B0 = 3.5 T) and strained (B0 = 4.4 T) regimes.
- Implementation Strategy: The simulations rely on instantaneous electron Ļ-rotations, justifying the proposed use of all-optical spin control methods, which offer picosecond switching speeds compatible with ultra-low temperature cryostats (ā¤4 K).
Technical Specifications
Section titled āTechnical Specificationsā| Parameter | Value | Unit | Context |
|---|---|---|---|
| Electron Gyromagnetic Ratio (Ī³e) | 28 | GHz/T | Hamiltonian Constant |
| Nuclear Gyromagnetic Ratio (Ī³n) | -8.46 | MHz/T | Hamiltonian Constant |
| Ground State Spin-Orbit Coupling (ASO) | 46 | GHz | Key mechanism enabling IC |
| Hyperfine Coupling (A||) | 70 | MHz | Parallel to SiV-axis |
| Hyperfine Coupling (Aā„) | 78 | MHz | Perpendicular to SiV-axis |
| Strain Anisotropy (Ī±, Ī²) | 150 | GHz | Strained Regime (Case B) |
| Operating Temperature | ā¤4 | K | Required for SiV- operation |
| Unstrained B0 Field (Case A) | 3.5 | T | Optimized for ĪĪø = 60Ā° (120Ā° change) |
| Strained B0 Field (Case B) | 4.4 | T | Optimized for ĪĪø = 90Ā° |
| Fastest Gate Duration (Unstrained X) | 209.06 | ns | Single-qubit X gate (F ā„ 0.99) |
| Slowest Gate Duration (Strained X) | 1296.50 | ns | Single-qubit X gate (F ā„ 0.99) |
| Simulated Gate Fidelity (F) | ā„0.98 | - | Achieved across all gates |
| Equivalent NMR Rabi Frequency | ~1.6 | MHz | Required for equivalent speed via direct NMR |
| Electron Hyperfine Field (Bhf) | ~4.14 | T | Field felt by 29Si nucleus |
Key Methodologies
Section titled āKey MethodologiesāThe methodology relies on numerical simulation and optimization of the 29SiV- spin Hamiltonian to achieve fast, high-fidelity Indirect Control (IC) gates.
- Hamiltonian Definition: The total Hamiltonian (H) was defined, including electron (He) and nuclear (Hn) Zeeman terms, hyperfine coupling (Hhf), spin-orbit coupling (HSO), and strain (Hstr).
- Regime Selection: Simulations were performed for two regimes:
- Unstrained (A): Ī± = Ī² = 0 GHz.
- Strained (B): Ī± = Ī² = 150 GHz (chosen to allow full electron Ļ-rotation).
- B0 Field Optimization: The static magnetic field (B0) was oriented at 54.7Ā° relative to the SiV axis (corresponding to the [100] vector orientation in a diamond sample) to maximize the change (ĪĪø) in the nuclear spin quantization axis (Bnet) upon electron spin flip.
- Gate Sequence Construction: Single-qubit gates (X, Y, Z, H, S, T) were constructed using a sequence of instantaneous electron Ļ-rotations (Ļ1, Ļ2, Ļ3, Ļ4) separated by free precession delays (Ļ1, Ļ2, Ļ3, Ļ4).
- Numerical Optimization: The gate parameters (delays Ļ) were optimized using Matlabās āSurrogate Optimizationā solver. The objective was to maximize the overlap (fidelity F) between the final time-evolved state and the target state, while minimizing the total gate time.
- Phase Control Implementation: Phase gates (Z, S, T) were achieved by allowing the nuclear spin to precess around the secondary quantization axis (BĪ²) during the delays, accumulating the necessary phase shift.
- Practical Implementation Justification: The use of instantaneous electron Ļ-rotations justifies the proposed use of all-optical control methods, which can achieve switching speeds potentially in the picosecond range, minimizing disturbance to the nuclear spin during the electron switching period.
Commercial Applications
Section titled āCommercial ApplicationsāThis research provides a critical pathway for developing robust, high-speed quantum information processing platforms based on diamond color centers.
- Quantum Computing: Enables fast, coherent two-axis control of intrinsic nuclear spin qubits (29Si) within the SiV- center, a fundamental requirement for universal quantum gate sets.
- Quantum Memory: Nuclear spins offer superior isolation and long coherence times compared to electron spins. This IC technique allows high-speed writing and reading of quantum information into these long-lived nuclear memory nodes.
- Scalable Quantum Registers: Utilizing the host nuclear spin (intrinsic to the defect) simplifies fabrication and scaling compared to relying on randomly occurring coupled 13C atoms.
- Cryogenic Quantum Devices: The proposed all-optical control method is highly compatible with ultra-low temperature environments (e.g., dilution refrigerators with cooling power of 10-500 ĀµW), avoiding the need for high-power microwave antennas.
- Transferable Technology: The methodology is expected to be applicable to other Group IV vacancy centers in diamond (e.g., Germanium-Vacancy (GeV) centers) that exhibit similar large spin-orbit coupling properties.
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 spinās 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.