Measurement of the excited-state transverse hyperfine coupling in NV centers via dynamic nuclear polarization

At a Glance

Metadata	Details
Publication Date	2017-05-15
Journal	Physical review. B./Physical review. B
Authors	Francesco Poggiali, Paola Cappellaro, Nicole Fabbri
Institutions	National Institute of Optics, Massachusetts Institute of Technology
Citations	25
Analysis	Full AI Review Included

6CCVD Technical Analysis & Quantum Material Solutions

Dynamic Nuclear Polarization in NV Centers for Quantum Computing

Analysis of: Measurement of the excited-state transverse hyperfine coupling in NV centers via dynamic nuclear polarization (arXiv:1612.04783v2)

This research successfully measures a critical, previously unknown parameter ($C_{\perp}$) within the Nitrogen-Vacancy (NV) center spin Hamiltonian, providing essential knowledge for robust control and initialization of NV-based quantum information systems. The methodology leverages the time-dependent dynamics of Dynamic Nuclear Polarization (DNP) in high-purity Single Crystal Diamond (SCD) to achieve this precision.

Executive Summary

Core Achievement: First direct experimental measurement of the excited-state transverse hyperfine coupling ($C_{\perp}$) between the electronic spin ($S=1$) and the intrinsic $^{14}$N nuclear spin ($I=1$) in the NV center.
Key Finding: The transverse coupling was precisely determined as $C_{\perp} = (-23 \pm 3)$ MHz, demonstrating significant anisotropy, which contradicts the often-assumed isotropic interaction (typically $-40$ MHz).
Methodology: Exploited the temporal dynamics of Dynamic Nuclear Polarization (DNP) near the Excited State Level Anti-Crossing (ESLAC), where transverse coupling induces electron-nuclear flip-flops.
Material Requirement: Research utilized ultra-high purity, electronic-grade Single Crystal Diamond (SCD) with ultra-low nitrogen (< 5 ppb) and natural $^{13}$C abundance (1.1%).
Technical Impact: Provides the required precise Hamiltonian parameters for enhanced modeling, initialization, and long-term coherence control of NV multi-spin systems.
Applications: Crucial data for advancing quantum computing, quantum memory, and NV-based magnetic sensing enhanced by polarized nuclear spin ensembles.

Technical Specifications

The experiment relies on precise control of spin states in isolated NV centers at room temperature, necessitating high-quality diamond material and high-fidelity pulse sequences.

Parameter	Value	Unit	Context
Material Basis	SCD, Electronic Grade	N/A	Low-strain bulk diamond
Intrinsic NV Nucleus	$^{14}$N ($I=1$)	N/A	Used for DNP mechanism
Nitrogen Concentration	< 5	ppb	Required for isolated single NV centers
Operating Temperature	Room Temperature	N/A	Standard NV operation
Excitation Wavelength	532	nm	Green laser source (optical pumping)
Magnetic Field Range ($B$)	200 to 420	G	Range used for polarization dynamics analysis
ESLAC Field	~510	G	Magnetic field defining the Excited State Level Anti-Crossing
Electronic Splitting ($D_e$)	1.42	GHz	Zero-field splitting (excited state)
Nuclear Quadrupole ($Q$)	-4.945	MHz	Intrinsic $^{14}$N property
Ground State Longitudinal ($A_{\parallel}$)	-2.162	MHz	Hyperfine coupling constant
Ground State Transverse ($A_{\perp}$)	-2.62	MHz	Hyperfine coupling constant
ES Transverse ($C_{\perp}$) - Measured	-23 ± 3	MHz	Key experimental result (first direct measurement)
MW $\pi/2$ Pulse Length	25-50	ns	High-speed electronic spin manipulation (Ramsey)
RF $\pi$ Pulse Length	~30	µs	Nuclear spin manipulation
DNP Timescale ($\tau$)	1 to 5	µs	Characteristic time-constant of nuclear polarization

Key Methodologies

The study measured the temporal evolution of the ground-state hyperfine level populations ($P_{I}$) under continuous optical pumping (DNP). This required a complex sequence combining optical, microwave (MW), and radiofrequency (RF) manipulation:

Initial State Preparation:
- System initialized using a long 20 µs optical pulse (532 nm) to partially polarize the NV electronic spin into an unbalanced mixed state (driving $m_s=0$ to $m_s \neq 0$).
Nuclear Spin Reversal:
- A 30 µs RF $\pi$ pulse, resonant with the $|0, +1\rangle_g \leftrightarrow |0, 0\rangle_g$ transition, was applied to co-herently reverse the populations of the $m_I = 0$ and $m_I = +1$ nuclear spin projections.
Dynamic Nuclear Polarization (DNP) Pumping:
- An optical pumping laser pulse of variable duration ($t$) at saturation power was applied. This induces electron-nuclear spin flip-flops near the ESLAC, driving polarization transfer from the electronic spin to the nuclear spin.
State Readout (Ramsey Spectroscopy):
- The resulting relative populations of the ground-state hyperfine sublevels ($|0, m_I\rangle_g$) were measured using a Ramsey sequence (two MW $\pi/2$ pulses separated by a variable free evolution time).
Data Extraction and Modeling:
- Experimental polarization dynamics were compared against theoretical simulations based on the generalized Liouville equation (Lindblad operator formalism).
- The unknown parameter, $C_{\perp}$, was extracted by minimizing the mean squared residuals ($\chi^{2}$) between the experimental polarization time constants ($\tau$) and the theoretical curves.

6CCVD Solutions & Capabilities

The successful replication and extension of this high-precision quantum research relies fundamentally on accessing diamond materials with exceptionally low impurity concentration, controlled defect environment, and superior surface quality. 6CCVD is an expert provider of the necessary custom MPCVD diamond solutions.

Applicable Materials for NV Center Physics

To replicate the ultra-pure, electronic-grade diamond used in this study (which contains intrinsic $^{14}$N NV centers at < 5 ppb), researchers require our premium Single Crystal Diamond (SCD) material.

6CCVD Material Solution	Specification & Suitability	Target Research Application
Optical Grade SCD	Ultra-low [N] (< 5 ppb) and low-strain characteristics necessary for isolating single NV centers.	DNP optimization, long coherence time experiments, high-fidelity quantum control.
Custom $^{15}$N SCD	Available SCD substrates with controlled $^{15}$N doping, enabling the study of $I=1/2$ nuclear spins for alternative DNP schemes.	Nuclear spin memory, enhanced quantum sensing using $I=1/2$ systems.
Heavy Boron-Doped PCD (BDD)	While not used in this specific study, BDD electrodes are critical for charge-state stabilization (NV$^{-}$ vs. NV$^{0}$) often required in DNP environments (Appendix C).	Charge stabilization layers, electrochemistry, high-power electronics.

Customization Potential & Engineering Support

The research utilized high-frequency MW and RF pulses via an antenna wire [33]. Integrating such structures requires precise diamond substrate geometry and, often, reliable metal contacts directly on the diamond surface.

6CCVD Capability	Application in NV Research
Custom Dimensions & Thickness	We provide SCD plates up to 125mm (PCD) and SCD thicknesses from 0.1 µm up to 500 µm, allowing flexible integration into confocal microscopy or cryo-systems.
High-Precision Polishing	Ultra-smooth surfaces (Ra < 1 nm for SCD) are crucial for minimizing optical scattering and maximizing photon collection efficiency necessary for sensitive NV readout.
Custom Metalization	We offer in-house deposition of thin-film metal stacks (e.g., Ti/Pt/Au, Ti/W/Cu) ideal for fabricating planar microwave strip lines or integrated RF/MW antennas directly onto the diamond surface for fast spin control.
Laser Micromachining	Our advanced laser cutting services can create precise features, trenches, or custom substrate shapes required for positioning MW/RF wires or integrating fluidic channels for sensing applications.
Engineering Consultation	6CCVD’s in-house PhD material scientists and engineers specialize in optimizing diamond growth recipes to meet highly specific requirements, such as controlled strain levels or alternative defect incorporation necessary to replicate or extend similar quantum memory and sensing projects.

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View Original Abstract

Precise knowledge of a quantum system’s Hamiltonian is a critical\npre-requisite for its use in many quantum information technologies. Here, we\nreport a method for the precise characterization of the non-secular part of the\nexcited-state Hamiltonian of an electronic-nuclear spin system in diamond. The\nmethod relies on the investigation of the dynamic nuclear polarization mediated\nby the electronic spin, which is currently exploited as a primary tool for\ninitializing nuclear qubits and performing enhanced nuclear magnetic resonance.\nBy measuring the temporal evolution of the population of the ground-state\nhyperfine levels of a nitrogen-vacancy center, we obtain the first direct\nestimation of the excited-state transverse hyperfine coupling between its\nelectronic and nitrogen nuclear spin. Our method could also be applied to other\nelectron-nuclear spin systems, such as those related to defects in silicon\ncarbide.\n

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Original Source

DOI: https://doi.org/10.1103/physrevb.95.195308