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	La Trobe University, The University of Melbourne
Citations	4
Analysis	Full AI Review Included

Executive Summary

This research investigates the effects of rapid physical rotation on the interaction between a central Nitrogen-Vacancy (NV) electron spin qubit and its surrounding ¹³C nuclear spin bath in diamond.

Objective: To determine if rapid physical rotation, analogous to Magic Angle Spinning (MAS) in Nuclear Magnetic Resonance (NMR), can suppress deleterious anisotropic spin interactions (decoherence) in a solid-state quantum system.
Experimental Setup: Natural abundance ¹³C CVD diamond containing NV centers was rotated at speeds up to 300,000 rpm (5.17 kHz) while subjected to an external, off-axis magnetic field (up to 40 G).
Primary Finding (Decoherence Mechanism): The rotation, combined with the off-axis field, strongly modulates the NV-¹³C hyperfine interaction. This modulation introduces rotation-dependent frequency modulation of the nuclear spin Larmor precession, leading to rapid ensemble dephasing.
Result: Instead of achieving rotational decoupling, the NV spin coherence (T₂^eff) rapidly collapses as the rotation speed and magnetic field tilt angle increase, demonstrating that the hyperfine modulation effect dominates over the desired decoupling of weaker homonuclear ¹³C-¹³C interactions.
Implications for Control: Conventional rotational averaging techniques are ineffective for the NV system at achievable speeds. New strategies, such as Magic Angle Hopping (MAH) or significantly faster rotation rates (greater than 6 million rpm), are required to mitigate the strong electron-nuclear hyperfine coupling.
Methodology: Spin-echo interferometry, synchronized with the rotation, was used to measure the coherence loss, supported by numerical simulations using a time-dependent disjoint-cluster model.

Technical Specifications

Parameter	Value	Unit	Context
Maximum Rotation Speed (f_rot)	300,000 (5.17)	rpm (kHz)	Experimental limit achieved for the diamond sample.
NV Zero-Field Splitting (D_zfs)	2870	MHz	Energy splitting between m_s = 0 and m_s = ±1 ground states.
Electron Gyromagnetic Ratio (γ_e/2π)	2.8	MHz/G	Used for calculating electron Zeeman splitting.
¹³C Gyromagnetic Ratio (γ_n/2π)	1071.5	Hz/G	Nuclear spin precession constant.
Maximum Applied Magnetic Field (B)	40	G	Field strength used to introduce off-axis tilt (θ_B).
Diamond Material	Natural Abundance ¹³C	CVD	Sample composition (98.9% ¹²C).
NV Ensemble Density	0.1	ppm	Typical nitrogen density in the sample.
Phenomenological T₂ Limit (T₂^phenom)	150	µs	Coherence limit due to other defects (e.g., P1 centers).
Microwave Rabi Frequency	5	MHz	Used for applying π/2 and π pulses.
Magic Angle (θ_m)	54.74	degrees	Angle required for motional averaging of dipolar coupling.
Homonuclear ¹³C-¹³C Coupling	10² - 10³	Hz	Weak intra-bath dipolar interactions.
NV-¹³C Hyperfine Coupling (Typical)	10⁵	Hz	Strong electron-nuclear interaction (6 million rpm equivalent).

Key Methodologies

Sample Preparation and Mounting: An optical-grade (111)-cut CVD diamond, containing an ensemble of NV centers, was mounted on an electric motor spindle. The NV axis was aligned to be nearly parallel (miscut < 0.2°) to the rotation (z) axis.
Optical Preparation and Readout: A confocal microscope setup was utilized. NV centers were initialized using 500 µW of green light and read out by collecting emitted red fluorescence directed to an avalanche photodiode.
Magnetic Field Control: Three pairs of current-carrying coils generated static magnetic fields (B) up to 40 G. The field direction was tilted relative to the rotation axis (θ_B) to introduce anisotropic averaging components.
Microwave Spin Control: A 20 µm copper wire, positioned 300 µm above the diamond surface, delivered microwave pulses (5 MHz Rabi frequency) to manipulate the NV electron spin state.
Spin-Echo Interferometry: The NV coherence was measured using a standard spin-echo sequence (π/2 - τ - π - τ - π/2). The sequence was synchronized with the diamond rotation to measure magnetic field components effectively up-converted to the rotation frequency (B_ac).
Coherence Time Extraction: The spin-echo time (T_R) was adjusted to coincide with the rotationally-shifted ¹³C contrast revival maxima. The effective spin coherence time (T₂^eff) was determined by fitting the decay envelope of the spin-echo contrast.
Numerical Simulation: A theoretical model based on the disjoint-cluster method was adapted to the time-dependent, non-secular Hamiltonian in the rotating frame. This model simulated the ensemble-averaged spin-echo signal for various bath configurations and rotation parameters.

Commercial Applications

This research provides critical insights for engineering quantum systems that involve mechanical motion or require robust spin coherence in noisy solid-state environments.

Quantum Sensing and Metrology:
- Diamond Gyroscopes: Directly relevant to developing NV-based gyroscopes, where the diamond sample itself is rotated. The findings define the limits of coherence and precision achievable under rotation.
- Nanoscale Magnetometry: Improving the precision of NV-based magnetometers by informing strategies to decouple the central qubit from the surrounding nuclear spin bath noise.
Solid-State Quantum Information Processing (QIP):
- Hybrid Spin Registers: Essential for designing robust quantum memory and computation architectures that rely on coupling the NV electron spin to nearby ¹³C nuclear spins. The work highlights the need for advanced control schemes to maintain coherence in dynamic environments.
Advanced Spin Control Techniques:
- Magic Angle Hopping (MAH): The study suggests MAH—where the magnetic field is rapidly reoriented rather than the sample spun extremely fast—as a feasible alternative for decoupling the strong electron-nuclear hyperfine interaction at achievable kHz rotation speeds.
Fundamental Physics of Motional Qubits: Applicable to emerging platforms such as levitated diamonds or particles in ion traps, where the quantum system possesses motional and rotational degrees of freedom that must be characterized and controlled.

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