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

At a Glance

Metadata	Details
Publication Date	2024-02-09
Journal	Frontiers in Quantum Science and Technology
Authors	Alexander Nizovtsev, Aliaksandr Pushkarchuk, S. A. Kuten, Dominik L. Michels, Dmitry Lyakhov
Institutions	Institute of Physical and Organic Chemistry, National Research Nuclear University MEPhI
Analysis	Full AI Review Included

Technical Documentation & Analysis: Indirect $^{13}$C J-Coupling in Diamond NV Systems

Executive Summary

This research confirms the necessity of analyzing the full indirect nuclear spin-spin interaction ($J$-coupling) tensor in diamond-based quantum systems, moving beyond the traditionally measured isotropic scalar constant ($J_{iso}$).

Critical Interaction: The study simulates the full $J$-coupling tensors ($J_{KL}$) for $^{13}$C nuclear spins in H-terminated diamond clusters, essential for high-resolution quantum sensing and memory applications.
Anisotropic Contributions: It is demonstrated that anisotropic contributions to the $J$-coupling tensor are essential for accurate characterization, particularly for nearest-neighbor ($N-N$) $^{13}$C pairs.
NV Center Influence: The presence of the negatively charged Nitrogen-Vacancy (NV) center significantly affects the $J$-coupling characteristics of proximal $^{13}$C pairs, leading to an increase of up to ~9% in diagonal tensor elements ($^{1}J_{KK}$).
Methodological Validation: The PBE0/UKS/pcJ-2 Density Functional Theory (DFT) level provided superior agreement with experimental $J_{iso}$ data (31.4 ± 0.5 Hz), validating the methodology for complex solid-state spin systems.
Material Requirement: Accurate experimental realization of these multi-qubit registers requires high-purity, isotopically controlled Single Crystal Diamond (SCD) to minimize decoherence and achieve the necessary sub-Hertz spectral resolution.
6CCVD Value Proposition: 6CCVD provides the necessary SCD materials with custom isotopic purity, precise dimensions, and advanced metalization capabilities required to replicate and scale this foundational quantum research.

Technical Specifications

The following hard data points were extracted from the simulation and experimental context:

Parameter	Value	Unit	Context
Experimental Isotropic J-coupling ($^{1}J_{iso}$)	31.4 ± 0.5	Hz	Nearest-Neighbor ($N-N$) $^{13}$C in Adamantane
Simulated $^{1}J_{iso}$ Range (Adamantane)	29.799 - 30.168	Hz	N-N $^{13}$C pairs, dependent on basis set
Anisotropic J-coupling ($A^{1}J$)	-12.1623	Hz	C1-C2 pair in Adamantane (Basis Set 2)
Simulated $^{1}J_{iso}$ Range (Cluster $C_{35}H_{36}$)	28.76 - 30.86	Hz	One-bond N-N pairs (Basis Set 2)
NV Center Effect on Diagonal Elements ($^{1}J_{KK}$)	~9	% Increase	Observed for C atoms nearest to the NV vacancy
Typical Direct Dipolar Coupling	~2	kHz	N-N $^{13}$C pairs in diamond
Required Spectral Resolution	Sub-Hertz (Hz-level)	Precision	Necessary for accurate NV sensor characterization
C-C Bond Length (Diamond)	~1.54	Å	Single covalent bond separation

Key Methodologies

The theoretical simulation of the full $J$-coupling tensors utilized advanced quantum chemistry techniques:

Cluster Modeling: The diamond lattice was modeled using H-terminated carbon clusters: Adamantane ($C_{10}H_{16}$), a larger cluster ($C_{35}H_{36}$), and a cluster hosting the negatively charged NV center ($C_{33}[NV]H_{36}$).
Geometry Optimization: Cluster geometries were optimized using the ORCA software package (version 5.0.3) at the B3LYP/UKS/def2/J/RIJCOSX level of theory.
DFT Calculation Levels: Two distinct levels of Density Functional Theory (DFT) were employed for $J$-coupling tensor calculation:
- Level 1: B3LYP/UKS/TZVPP (Basis Set 1).
- Level 2 (Advanced): PBE0/UKS/pcJ-2 (Basis Set 2), which is specifically optimized for spin-spin coupling constant calculations and yielded better agreement with experimental data.
Tensor Decomposition: The total $J_{KL}$ tensor was calculated by summing contributions from five components: Diamagnetic, Paramagnetic, Fermi-Contact (FC), Spin-Dipolar (SD), and the SD/FC cross-term.
Coordinate System Transformation: Calculated matrices were transformed to a coordinate system where the Z-axis was aligned along the specific $^{13}$C-$^{13}$C bond, allowing for the extraction of the essential diagonal elements ($^{1}J_{XX}$, $^{1}J_{YY}$, $^{1}J_{ZZ}$) and the asymmetric part ($A^{1}J$).

6CCVD Solutions & Capabilities

This research highlights the need for ultra-high-quality, customized diamond materials to transition theoretical findings into functional quantum devices. 6CCVD is uniquely positioned to supply the necessary materials and engineering services.

Research Requirement (Nizovtsev et al.)	6CCVD Solution & Capability	Technical Advantage
Isotopic Purity: Need for controlled $^{13}$C concentration to achieve long coherence times for quantum memory.	Isotopically Engineered Single Crystal Diamond (SCD): We supply SCD wafers with precise isotopic control, including ultra-low $^{13}$C concentration (< 100 ppm) or specific enrichment, critical for minimizing decoherence.	Enables the realization of the minute-long coherence times reported for $^{13}$C-$^{13}$C dimers, essential for robust quantum registers.
Substrate Dimensions: Need for stable, high-quality platforms for NV center creation and device integration.	Custom SCD Substrates: Available in thicknesses ranging from 0.1 µm up to 500 µm (SCD) and bulk substrates up to 10 mm. We offer custom dimensions up to 125 mm (PCD).	Provides the necessary structural integrity and flexibility for both shallow NV sensing and deep NV quantum memory applications.
Surface Quality: Requirement for H-termination (used in simulation) and high-precision NV creation.	Ultra-Low Roughness Polishing: SCD surfaces polished to Ra < 1 nm. Inch-size PCD wafers polished to Ra < 5 nm.	Ensures minimal surface defects, which is vital for achieving the high spectral resolution (sub-Hertz) required for characterizing spin clusters near the surface.
Device Integration: Need for on-chip microwave/RF structures to control spin states.	Advanced Metalization Services: Internal capability for custom deposition of Au, Pt, Pd, Ti, W, and Cu contacts.	Facilitates the integration of high-frequency control lines necessary for initializing, manipulating, and reading out the NV and $^{13}$C spin states, as required by the experimental context.
Scaling Potential: Need to move from small clusters to scalable quantum architectures.	Large-Area Polycrystalline Diamond (PCD): Custom PCD plates/wafers available up to 125 mm diameter.	Supports the scaling of quantum magnetic sensing and memory technologies beyond laboratory-scale clusters.

Engineering Support

6CCVD’s in-house PhD team specializes in MPCVD growth and post-processing techniques tailored for quantum applications. We offer authoritative professional consultation on material selection, isotopic control, and surface preparation necessary to replicate or extend this research on NV-based quantum sensing and memory projects.

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

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

Original Source

DOI: https://doi.org/10.3389/frqst.2024.1332264

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