Tunable gyromagnetic augmentation of nuclear spins in diamond

At a Glance

Metadata	Details
Publication Date	2022-01-13
Journal	Physical review. B./Physical review. B
Authors	R. M. Goldblatt, A. Martin, A. A. Wood
Institutions	The University of Melbourne
Citations	4
Analysis	Full AI Review Included

Technical Documentation & Analysis: Tunable Gyromagnetic Augmentation of Nuclear Spins in Diamond

Executive Summary

This research demonstrates a critical advancement in solid-state quantum computing by achieving rapid, tunable quantum control over “dark” P1 nuclear spins (¹⁴N) in diamond at room temperature.

Core Achievement: Fast quantum control of P1 nuclear spins was realized by leveraging hyperfine coupling to the P1 electron spin, which significantly augments the nuclear gyromagnetic ratio (α).
Tunability: The augmentation factor (α) is highly dependent on the external magnetic field (B), enabling dynamic tuning of the nuclear spin interaction regime.
Performance: Fast quantum gate operations were demonstrated at low magnetic fields (< 100 G), achieving Rabi frequencies up to 1.82 MHz, comparable to typical P1 or NV electron spin frequencies.
Methodology: Double Electron-Electron Resonance (DEER) spectroscopy, coupled with Rabi oscillation measurements, was used to characterize the P1 spin bath and quantify the augmentation factor.
Material Requirement: The experiment utilized a Type 1b, (111)-cut diamond with low nitrogen (1 ppm N) and natural ¹³C abundance (1.1%).
Quantum Significance: This work establishes P1 nuclear spins as viable, long-lived qubits whose control speed can be dynamically enhanced, addressing the fundamental challenge of accessing isolated nuclear spins.

Technical Specifications

The following hard data points were extracted from the research paper, detailing the material and performance metrics achieved.

Parameter	Value	Unit	Context
Diamond Type	Type 1b	N/A	Sample used for experiment
Crystal Orientation	(111)-cut	N/A	Sample orientation
Nitrogen (N) Concentration	1	ppm	P1 center precursor concentration
¹³C Natural Abundance	1.1	%	Sample composition
Operating Temperature	Room	°C	Experiment conducted at ambient temperature
External Magnetic Field (B) Range	10 to 100	G	Range where augmentation is significant
Maximum Rabi Frequency (Ω_max)	1.82	MHz	Observed at B = 20 G for transition de
Maximum Oscillation Amplitude (S(0)_max)	0.012	N/A	Observed at B = 20 G
Electron Gyromagnetic Ratio (γ_e/2π)	-2.8	MHz/G	P1 center electron spin
¹⁴N Nuclear Gyromagnetic Ratio (γ_N/2π)	307.7	Hz/G	Bare nuclear spin value
Axial Hyperfine Coupling (A_\|\|/2π)	114	MHz	P1 center interaction parameter
Transverse Hyperfine Coupling (A_⊥/2π)	81.34	MHz	P1 center interaction parameter

Key Methodologies

The experimental characterization of the P1 nuclear spin augmentation relied on precise material handling and advanced microwave/radiofrequency control techniques.

Material Selection and Mounting: A Type 1b, (111)-cut diamond sample (1 ppm N, 1.1% ¹³C) was mounted on a precision rotation stage (electric motor spindle) to control the alignment relative to the magnetic field.
Magnetic Field Generation: Current-carrying coils were used to generate a variable external magnetic field (B) up to 100 G, aligned along the NV axis (z-axis).
Control Field Delivery: Microwaves (MW) for NV driving and Radiofrequency (RF) fields for P1 control were generated by crossed wires (20 µm and 50 µm diameters, respectively). RF pulses were produced using an I/Q modulated vector signal generator.
DEER Spectroscopy: Double Electron-Electron Resonance (DEER) spectroscopy was employed to characterize the dark P1 spin bath surrounding the NV centers.
Pulse Sequence: A spin-echo pulse sequence was applied to the NV ensemble, with the free evolution time fixed at a ¹³C revival time (45-65 µs) to maintain signal visibility. An RF π-pulse was swept in frequency to recouple resonant spins.
Rabi Oscillation Measurement: The P1 nuclear spin Rabi frequency (Ω) was measured by varying the length of the resonant RF pulse at different external magnetic field strengths (10 G to 100 G).
Augmentation Factor Calculation: Measured Rabi frequencies and amplitudes were normalized and compared against theoretical calculations of the augmentation factor (α) derived from the diagonalized P1 Hamiltonian.

6CCVD Solutions & Capabilities

The successful replication and extension of this research—particularly in developing scalable P1-based quantum registers—requires ultra-high purity diamond materials with precise control over defect concentration and crystal orientation. 6CCVD is uniquely positioned to supply the necessary custom MPCVD diamond solutions.

Applicable Materials

To replicate or extend the fast quantum control demonstrated in this paper, researchers require diamond with extremely low intrinsic nitrogen and precise crystal orientation.

Research Requirement	6CCVD Material Solution	Key Specification
High Purity Substrate	Optical Grade Single Crystal Diamond (SCD)	Ultra-low N concentration (< 1 ppm, down to ppb levels) to minimize background decoherence.
Specific Defect Density	Custom Doped SCD	Precise control over N concentration (e.g., 1 ppm used in the paper) to optimize P1 center density for ensemble measurements or reduce N for single-qubit isolation.
Crystal Orientation	Custom (111) SCD Wafers	SCD plates available in standard (100) or custom (111) orientation, crucial for aligning the NV/P1 axis with the external magnetic field.
Isotopic Control	Isotopically Pure SCD	Availability of 99.99% ¹²C SCD to eliminate ¹³C-induced decoherence, or enriched ¹³C SCD for specific quantum register architectures.

Customization Potential

The integration of quantum control fields (MW/RF wires) and the need for specific sample geometries are fully supported by 6CCVD’s advanced fabrication capabilities.

Custom Dimensions and Cuts: 6CCVD provides SCD plates up to 10x10 mm and PCD wafers up to 125 mm. We offer precision laser cutting and shaping services to match specific experimental geometries required for RF/MW integration.
Advanced Polishing: The experiment relies on high-fidelity optical preparation and readout. 6CCVD guarantees ultra-smooth surfaces:
- SCD Polishing: Surface roughness (Ra) < 1 nm.
- PCD Polishing: Surface roughness (Ra) < 5 nm (for inch-size wafers).
Integrated Metalization: For direct integration of the control wires (20 µm and 50 µm diameters mentioned in the paper) or creation of on-chip transmission lines, 6CCVD offers in-house metalization services, including:
- Standard Quantum Contacts: Au, Pt, Pd, Ti, W, and Cu.
- Patterning: Custom lithographic patterning for precise RF/MW delivery structures.

Engineering Support

This research highlights the complex interplay between material properties (N concentration, ¹³C abundance) and quantum control parameters (magnetic field, RF frequency).

Material Consultation: 6CCVD’s in-house PhD team specializes in optimizing MPCVD growth recipes to meet the exact specifications for Tunable Gyromagnetic Augmentation projects. We assist researchers in selecting the optimal N concentration and isotopic purity to balance coherence time and control speed.
Global Logistics: We ensure reliable, timely delivery of sensitive diamond materials worldwide, offering DDU (Delivery Duty Unpaid) as default and DDP (Delivery Duty Paid) options for seamless international shipping.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Nuclear spins in solids exhibit long coherence times due to the small nuclear gyromagnetic ratio. This weak environmental coupling comes at the expense of slow quantum gate operations, which should be as fast as possible for many applications in quantum information processing and sensing. In this work, we use nitrogen-vacancy (NV) centers in diamond to probe the nuclear spins within dark paramagnetic nitrogen defects (P1 centers) in the diamond lattice. The gyromagnetic ratio of the P1 nuclear spin is augmented by hyperfine coupling to the electron spin, resulting in greatly enhanced coupling to radiofrequency control fields. We then demonstrate that this effect can be tuned by variation of an external magnetic field. Our work identifies regimes in which we are able to implement fast quantum control of dark nuclear spins, and lays the foundations for further inquiry into rapid control of long-lived spin qubits at room temperature.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.105.l020405