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6CCVD Research

Indirect interaction of 13C nuclear spins in diamond with NV centers - simulation of the full J-coupling tensors

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2024-02-09
JournalFrontiers in Quantum Science and Technology
AuthorsAlexander Nizovtsev, Aliaksandr Pushkarchuk, S. A. Kuten, Dominik L. Michels, Dmitry Lyakhov
InstitutionsNational Research Nuclear University MEPhI, Institute of Physical and Organic Chemistry
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research focuses on simulating the full indirect nuclear spin-spin interaction (J-coupling) tensors for 13C nuclear spins in diamond, a critical parameter previously neglected in studies utilizing Nitrogen-Vacancy (NV) centers for quantum technologies.

  • Core Achievement: Simulation of the full, second-rank J-coupling tensors (JKL) for nearest-neighbor (N-N) 13C-13C pairs in H-terminated diamond clusters, including models hosting a negatively charged NV center (C33[NV]H36).
  • Anisotropy is Key: The study confirms that the anisotropic contributions to the J-coupling tensor are essential and cannot be ignored, challenging the traditional reliance solely on the isotropic scalar constant (Jiso).
  • NV Center Influence: The presence of the NV center significantly affects J-coupling characteristics, causing an increase of up to ~9% in the diagonal elements (JKK) for 13C pairs located near the NV vacancy.
  • Methodology Validation: Two levels of Density Functional Theory (DFT) were used (B3LYP/UKS/TZVPP and PBE0/UKS/pcJ-2). The PBE0/UKS/pcJ-2 level provided results (Jiso ~30.1 Hz) closest to the available experimental value (31.4 ± 0.5 Hz).
  • Engineering Impact: The resulting full J-coupling tensors provide necessary input for highly accurate spin Hamiltonians, enabling the development of NV-based quantum sensors and quantum memories with sub-Hertz spectral resolution.

Technical Specifications

Section titled “Technical Specifications”

Data extracted from DFT simulations of 13C-13C J-coupling tensors in diamond-like clusters (C10H16, C35H36, C33[NV]H36). Calculations used the PBE0/UKS/pcJ-2 basis set (Basis 2) unless otherwise noted.

ParameterValueUnitContext
Experimental 1Jiso (N-N 13C)31.4 ± 0.5HzIsotropic J-coupling for nearest-neighbor 13C-13C in diamond (Adamantane).
Simulated 1Jiso (N-N 13C)30.018 - 30.168HzRange of isotropic J-coupling for N-N pairs in C10H16 (Adamantane).
Anisotropic Component (A1J)-12.1623HzAsymmetric part of the J-coupling tensor for the C1-C2 pair in Adamantane.
Nearest-Neighbor Dipolar Coupling~2kHzDirect dipole-dipole coupling for parallel-oriented N-N 13C pairs.
NV Center Perturbation (JKK)~9%Increase in diagonal JKK elements for 13C pairs nearest to the NV vacancy (e.g., C4, C5, C6 atoms in C33[NV]H36).
C-C Bond Length~1.54AngstromNearest-neighbor covalent bond separation in diamond.
Distant 13C-13C Jiso1.6 to 2HzIsotropic J-coupling for non-nearest-neighbor pairs (e.g., Jiso(bh-b) or Jiso(bh-bh)).

Key Methodologies

Section titled “Key Methodologies”

The indirect J-coupling tensors were calculated using quantum chemistry software (ORCA) applied to H-terminated diamond clusters, modeling the bulk diamond environment.

  1. Cluster Selection: Three H-terminated diamond-like clusters were modeled:
    • C10H16 (Adamantane) for baseline validation.
    • C35H36 (Larger diamond fragment).
    • C33[NV]H36 (Cluster hosting the negatively charged NV center).
  2. Geometry Optimization: Cluster geometries were optimized using the ORCA package at the B3LYP/UKS/def2/J/RIJCOSX level of theory.
  3. DFT Calculation Levels: Full J-coupling tensors (JKL) for all 13C-13C pairs were simulated using two distinct Density Functional Theory (DFT) levels:
    • Level 1: B3LYP/UKS/TZVPP.
    • Level 2 (Preferred): PBE0/UKS/pcJ-2 (Hybrid DFT level utilizing a specialized pcJ-2 segmented contracted basis set designed for spin-spin coupling constants).
  4. Tensor Decomposition: The total JKL tensor was calculated as the sum of five partial contributions: Diamagnetic, Paramagnetic, Fermi-Contact (FC), Spin-Dipolar (SD), and SD/FC cross-terms.
  5. Coordinate System Transformation: Calculated matrices were transformed to a diagonal form where the Z-axis was aligned along the specific C-C bond, facilitating the extraction of the isotropic scalar constant (Jiso) and the asymmetric/anisotropic part (A1J).

Commercial Applications

Section titled “Commercial Applications”

The detailed simulation data on J-coupling is foundational for advancing quantum technologies that rely on precise control and characterization of nuclear spin environments in diamond.

  • Quantum Memory and Registers:
    • Application: Designing robust solid-state quantum memories using coupled 13C nuclear spins (dimers or clusters) near an NV center.
    • Relevance: Accurate J-coupling data is essential for modeling the full spin Hamiltonian, allowing for the design of precise microwave and radiofrequency pulses necessary for initializing, controlling, and reading out the quantum states of 13C qubits.
  • Nanoscale Quantum Sensing (Magnetometry):
    • Application: Implementing highly sensitive magnetometers and NMR spectrometers using single NV centers to detect and image individual 13C nuclear spins with sub-Angstrom resolution.
    • Relevance: Consideration of anisotropic J-coupling is necessary for achieving the highest possible spectral resolution (sub-Hertz) required for detailed characterization of the spin environment.
  • Chemical Structure Analysis:
    • Application: Developing nanoscale NV-based sensors for the detection and structural determination of molecules or radicals adsorbed on the diamond surface.
    • Relevance: The J-coupling data helps interpret NMR spectra in the zero-to ultra-low-field (ZULF) regime, where internal spin interactions dominate the spectral features.
  • Solid-State NMR Development:
    • Application: Improving theoretical models for solid-state NMR spectroscopy, especially concerning orientation-dependent interactions in crystalline materials.
    • Relevance: The simulation of full J-coupling tensors (JKL) provides critical data for interpreting NMR lineshapes in fixed crystal orientations.
View Original Abstract

Recent experiments on the detection, imaging, characterization and control of multiple 13 C nuclear spins, as well as of individual 13 C- 13 C dimers in diamond using a single nitrogen-vacancy (NV) center as a sensor, along with the impressive progress in increasing the spectral resolution of such sensor (up to sub-Hertz), have created a request for detailed knowledge of all possible spin interactions in the studied systems. Here, we focus on the indirect interaction ( J -coupling) of 13 C nuclear spins in diamond, which was not previously taken into account in studies of NV centers. Using two different levels of the density functional theory (DFT), we simulated the full tensors n J KL (K, L = X, Y,Z), describing n-bond J -coupling of nuclear spins 13 C in H-terminated diamond-like clusters C 10 H 16 (adamantane) and C 35 H 36 , as well as in the cluster C 33 [NV − ]H 36 hosting the negatively charged NV − center. We found that, in addition to the usually considered isotropic scalar n J -coupling constant, the anisotropic contributions to the n J -coupling tensor are essential. We also showed that the presence of the NV center affects the J -coupling characteristics, especially in the case of 13 C- 13 C pairs located near the vacancy of the NV center.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2018 - One-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environment [Crossref]
  2. 2019 - Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor [Crossref]
  3. 2008 - Indirect spin-spin coupling constants in CH4, SiH4 and GeH4-Gas-phase NMR experiment and ab initio calculations [Crossref]
  4. 2018 - Quantum technologies with optically interfaced solid-state spins [Crossref]
  5. 2020 - Sensitivity optimization for NV-diamond magnetometry [Crossref]
  6. 2022 - Entanglement of spin-pair qubits with intrinsic dephasing times exceeding a minute [Crossref]
  7. 2016 - Zero-to ultralow-field NMR [Crossref]
  8. 2017 - Quantum sensing with arbitrary frequency resolution [Crossref]
  9. 2019 - A ten-qubit solid-state spin register with quantum memory up to one minute [Crossref]
  10. 2020 - Hyperpolarization-enhanced NMR spectroscopy with femtomole sensitivity using quantum defects in diamond [Crossref]

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