Anisotropic electron-nuclear interactions in a rotating quantum spin bath

At a Glance

Metadata	Details
Publication Date	2021-08-13
Journal	Physical review. B./Physical review. B
Authors	A. A. Wood, R. M. Goldblatt, R. P. Anderson, Lloyd C. L. Hollenberg, R. E. Scholten
Institutions	Centre for Quantum Computation and Communication Technology, The University of Melbourne
Citations	4
Analysis	Full AI Review Included

Technical Documentation & Analysis: Anisotropic Electron-Nuclear Interactions in a Rotating Quantum Spin Bath

Executive Summary

This research investigates the critical interaction between the Nitrogen-Vacancy (NV) electron spin qubit and the surrounding ¹³C nuclear spin bath in diamond under rapid physical rotation and off-axis magnetic fields.

Core Mechanism: Physical rotation of the diamond (up to 300,000 rpm) modulates the anisotropic NV-¹³C hyperfine interaction.
Decoherence Effect: This modulation introduces rapid decoherence (dephasing) into the system via rotation-dependent frequency modulation of the nuclear spin Larmor precession.
Experimental Limitation: The observed rapid dephasing, coupled with the inherent noise from the natural abundance ¹³C material used, obscures the potential observation of weaker homonuclear decoupling effects (like Magic Angle Spinning).
Material Implication: The study utilized natural abundance ¹³C CVD diamond, resulting in a stationary coherence time ($T_2^{phenom}$) limited to approximately 150 µs due to paramagnetic nitrogen (P1) centers and the noisy spin bath.
Future Direction: To successfully implement rotational decoupling schemes (e.g., Magic Angle Hopping) or observe coherent rotational effects, the research requires ultra-high purity, isotopically enriched ¹²C diamond substrates.
6CCVD Value Proposition: 6CCVD specializes in providing the necessary high-ppurity, isotopically enriched Single Crystal Diamond (SCD) and custom metalization required to mitigate spin bath noise and enable next-generation quantum control experiments.

Technical Specifications

Parameter	Value	Unit	Context
Maximum Rotation Speed ($\omega_{rot}$)	300,000 (8.33)	rpm (kHz)	Physical rotation rate of the diamond sample.
Magnetic Field Strength (B)	20, 40	G	Applied off-axis field strengths tested.
Magnetic Field Tilt Angle ($\theta_B$)	Up to 40-50	°	Angle between the NV axis and the magnetic field.
NV Zero-Field Splitting ($D_{zfs}$)	2870	MHz	Ground state splitting of the NV center.
Electron Gyromagnetic Ratio ($\gamma_e/2\pi$)	2.8	MHz/G	Used for calculating Zeeman splitting.
¹³C Gyromagnetic Ratio ($\gamma_n/2\pi$)	1071.5	Hz/G	Used for calculating nuclear Larmor precession.
Diamond Material Used	98.9% ¹²C (Natural Abundance ¹³C)	CVD Diamond	Sample used in the experiment.
Sample Cut/Miscut	(111)	Crystal Plane	Miscut angle < 0.2° relative to the rotation axis.
Phenomenological Coherence Time ($T_2^{phenom}$)	150	µs	Stationary coherence limit due to P1 centers/defects.
Microwave Control Wire Distance	300	µm	Distance of the 20 µm copper wire above the diamond surface.

Key Methodologies

The experiment utilized a highly specialized setup combining high-speed mechanical rotation with advanced quantum control techniques.

Material Preparation: An optical-grade CVD diamond sample, (111)-cut with a miscut angle of < 0.2°, was selected to align the NV axis nearly parallel to the rotation axis.
Physical Rotation System: The diamond was mounted on an electric motor capable of achieving rotation speeds up to 350,000 rpm (8.33 kHz).
Magnetic Field Generation: Three pairs of current-carrying coils were used to generate static magnetic fields up to 40 G, allowing for precise control of the off-axis tilt angle ($\theta_B$).
Microwave Control: Microwave fields (Rabi frequencies of 5 MHz) were applied using a 20 µm copper wire positioned 300 µm above the diamond surface.
Optical Readout: A confocal microscope focused 500 µW of green light onto the rotation center to prepare the NV ensemble, and collected red fluorescence via an avalanche photodiode for readout.
Coherence Measurement Technique: Spin-echo interferometry was employed, with microwave pulses synchronized to the rotation period, to measure the coherence of the rotating NV ensemble.
Synchronization: The spin-echo time ($T_R$) was precisely set to match integer multiples of the rotationally-shifted ¹³C contrast revival time to ensure overlap with coherence revivals.

6CCVD Solutions & Capabilities

This research demonstrates the critical need for ultra-pure, engineered diamond substrates to advance quantum control using motional averaging. 6CCVD provides the specialized MPCVD materials and fabrication services necessary to overcome the limitations encountered in this study.

Applicable Materials

To replicate and extend this research, specifically to eliminate the noisy spin bath and observe the subtle effects of rotational decoupling, the following 6CCVD materials are required:

Research Requirement	6CCVD Material Recommendation	Key Benefit for Application
Mitigate ¹³C Spin Bath Noise (Paper used 98.9% ¹²C)	High Purity SCD (99.999% ¹²C)	Extends $T_2$ coherence times significantly beyond 150 µs, allowing observation of rotational decoupling effects obscured by rapid dephasing.
Precise Crystal Orientation (Used (111)-cut, < 0.2° miscut)	Optical Grade SCD Wafers	Guaranteed precise crystallographic orientation and superior surface finish (Ra < 1 nm) critical for alignment with the high-speed rotation axis.
Integrated Quantum Control (Used external 20 µm copper wire)	SCD with Custom Metalization	Enables direct fabrication of integrated microwave strip lines (e.g., Ti/Pt/Au, Cu) onto the diamond surface for enhanced Rabi frequency and control fidelity.
Scaling and Substrate Thickness (Used small sample)	Thick SCD Substrates (up to 10 mm)	Provides robust mechanical stability necessary for high-speed rotation experiments (up to 350,000 rpm) and future scaling.

Customization Potential

The experimental setup required precise integration of magnetic field coils and microwave delivery systems. 6CCVD’s in-house capabilities directly support the customization needed for such advanced quantum experiments:

Custom Dimensions: We provide SCD plates and PCD wafers in custom dimensions up to 125 mm, ensuring optimal fit for specialized motor spindles and experimental chambers.
Precision Polishing: Our SCD material features polishing down to Ra < 1 nm, minimizing surface defects that can contribute to decoherence and ensuring high optical quality for NV center preparation and readout.
Integrated Metalization: 6CCVD offers internal metalization services (Au, Pt, Pd, Ti, W, Cu) for direct deposition of microwave transmission lines or electrodes onto the diamond surface, simplifying the integration of quantum control structures compared to external wire setups.

Engineering Support

The study of low-field dynamics and motional averaging in the NV-¹³C system is highly complex. 6CCVD’s in-house PhD team can assist with material selection for similar Quantum Sensing and Rotational Control projects, specifically advising on:

Isotopic Purity Optimization: Determining the optimal ¹²C enrichment level required to achieve target $T_2$ coherence times for observing subtle rotational effects.
Defect Engineering: Controlling nitrogen concentration (P1 centers) and NV density to balance ensemble averaging requirements with minimizing background decoherence.
Substrate Geometry: Designing custom plate dimensions and precise crystallographic cuts ((111) or other orientations) for specific rotational dynamics experiments.

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

View Original Abstract

The interaction between a central qubit spin and a surrounding bath of spins is critical to spin-based solid-state quantum sensing and quantum information processing. Spin-bath interactions are typically strongly anisotropic, and rapid physical rotation has long been used in solid-state nuclear magnetic resonance to simulate motional averaging of anisotropic interactions, such as dipolar coupling between nuclear spins. Here, we show that the interaction between electron spins of nitrogen-vacancy centers and a bath of C13 nuclear spins in a diamond rotated at up to 300 000 rpm introduces decoherence into the system via frequency modulation of the nuclear spin Larmor precession. The presence of an off-axis magnetic field necessary for averaging of the dipolar coupling leads to a rotational dependence of the electron-nuclear hyperfine interaction, which cannot be averaged out with experimentally achievable rotation speeds. Our findings offer new insights into the use of physical rotation for quantum control with implications for quantum systems having motional and rotational degrees of freedom that are not fixed.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.104.085419

References

2014 - Quantum Information Processing with Diamond: Principles and Applications