Non-flipping13C spins near an NV center in diamond - hyperfine and spatial characteristics by density functional theory simulation of the C510[NV]H252cluster

At a Glance

Metadata	Details
Publication Date	2018-01-19
Journal	New Journal of Physics
Authors	A. P. Nizovtsev, S. Ya. Kilin, A. L. Pushkarchuk, V. A. Pushkarchuk, S.A. Kuten
Institutions	Center for Integrated Quantum Science and Technology, B.I. Stepanov Institute of Physics
Citations	39
Analysis	Full AI Review Included

Technical Documentation and Quantum Brief

Robust NV-¹³C Spin Systems for Room-Temperature Quantum Memory

The analyzed research utilizes Density Functional Theory (DFT) simulation confirmed by experimental results to identify specific lattice sites within isotopically engineered single crystal diamond (SCD) where intrinsic ¹³C nuclear spins exhibit exceptionally long coherence times when coupled to Nitrogen-Vacancy (NV) centers. This discovery provides crucial, pre-validated coordinates for robust, non-flipping quantum memory elements essential for room-temperature quantum computing and sensing applications.

Executive Summary

Core Finding: DFT simulations of the C₅₁₀[NV]H₂₅₂ cluster systematically located ¹³C nuclear spin positions exhibiting negligible hyperfine-induced flipping rates (non-flipping spins).
Mechanism: Exceptional spin stability (long lifetimes, τ₀) is attributed to the near-symmetric local electron spin density distribution, resulting in a negligible off-diagonal hyperfine tensor component (T_nd ≈ 0).
Identified Classes: Two major stability classes were found: “axial” positions (on the NV symmetry axis) yielding lifetimes up to 10¹⁰ (effectively non-flipping) and 18 “non-axial near-stable” positions yielding lifetimes 2-4 orders of magnitude greater than unstable sites (τ₀ ≈ 10³ to 10⁴).
Spatial Location: The newly discovered non-axial near-stable ¹³C atoms are located primarily in the diamond bilayer perpendicular to the NV axis and passing through the NV vacancy.
Experimental Validation: Special experiments on 0.1% ¹³C engineered diamond successfully confirmed the predicted hyperfine characteristics (A_ZZ and T_nd) and demonstrated nuclear spin lifetimes of approximately 4 seconds at B=340 Gauss.
Material Requirement: Replicating and advancing this work requires high-purity, isotopically engineered Single Crystal Diamond (SCD) with precisely controlled, low ¹³C abundance and high NV center alignment (e.g., in (111) oriented wafers).

Technical Specifications

Parameter	Value	Unit	Context
Simulated Cluster Size	C₅₁₀[NV]H₂₅₂	Atoms	DFT model for NV center environment
NV Charge State (Sim.)	Singly Negative (S=1)	N/A	Triplet Ground State used for DFT
Target ¹³C Abundance (Exp.)	0.1	%	Engineered diamond used for validation
External Magnetic Field (Exp.)	340	Gauss	Used for experimental lifetime measurement (B
Maximum Calculated ¹³C Lifetime (τ₀)	1e+10	N/A (Unitless 1/Γ₀)	C505 (axial position), representing negligible flipping
Near-Stable Lifetime Range (τ₀)	10³ to 10⁴	N/A (Unitless 1/Γ₀)	Non-axial families St1-St4
Experimentally Measured Lifetime	4	seconds	Nuclear spin lifetime (St3/St4 family match) at 340 Gauss
Axial HFI Splitting (Δ₀)	194.0	kHz	C7 position (highest axial HFI)
Non-Axial HFI Splitting (Δ₀)	1001.8	kHz	St1 family (highest non-axial HFI average)
Experimental Diagonal HFI (A_ZZ)	-49.1 ± 0.3	kHz	Match for non-axial St3/St4 family
Experimental Off-Diagonal HFI (T_nd)	1.4 ± 0.1	kHz	Determined via dynamical decoupling spectroscopy
NV Z-Coordinate (C7)	6.47	Å	Axial position distance from N atom
C7 Distance from Z-Axis (R_CXY)	0	Å	Confirms axial alignment
St1 Average Distance from Z-Axis (R_CXY)	4.45	Å	Confirms non-axial position

Key Methodologies

The robust characterization of NV-¹³C spin systems relied on a combination of high-fidelity computational chemistry and sensitive solid-state quantum measurements.

DFT Cluster Simulation:
- The H-terminated diamond cluster C₅₁₀[NV]H₂₅₂ was modeled using DFT/B3LYP/UKS/MINI/3-21G theory.
- Calculations targeted the singly negatively charged NV center in its S=1 triplet ground state.
- The full hyperfine interaction (hfi) matrices (A_KL) were calculated for all 510 possible ¹³C lattice sites relative to the NV center axis (NV-PACS).
Stability Metric Calculation:
- The ¹³C nuclear spin flipping rate (Γ₀) and inverse lifetime (τ₀ = 1/Γ₀) were calculated based on the off-diagonal hyperfine component (T_nd), which is the primary determinant of coherence loss.
- Geometric analysis of the local e-spin density (ρ^s) distribution was performed to understand the local symmetry that causes T_nd ≈ 0 in the stable positions.
Experimental Material Preparation:
- A single NV center was measured in isotopically engineered CVD diamond containing a low ¹³C abundance (0.1%) to reduce background spin noise.
- The material was likely (111)-oriented to ensure highly aligned NV centers, critical for robust control.
Quantum Measurement Techniques:
- Electron Nuclear Double Resonance (ENDOR): Used to determine the strength of the diagonal hyperfine component (A_ZZ) by measuring the hfi-induced splitting (Δ^±) of the electron spin sublevels (m_s=0 and m_s=-1) under a static magnetic field (B=340 Gauss).
- Dynamical Decoupling Spectroscopy: Employed to measure the off-diagonal component (T_nd), which drives the nuclear spin flips, by tracking the resonant interaction between the electron spin and the nuclear spin bath.

6CCVD Solutions & Capabilities

This research confirms the critical role of material engineering—specifically isotopic control and high crystalline purity—in realizing practical, solid-state quantum memory devices. 6CCVD is uniquely positioned to supply the foundational diamond required to replicate, confirm, and extend these quantum breakthroughs.

Applicable Materials for Robust NV-¹³C Systems

To leverage the DFT predictions for low-flipping ¹³C sites, researchers require high-quality CVD diamond substrates with stringent isotopic control and superior surface finish.

6CCVD Material	Application Relevance	Key Capabilities
Isotopic Single Crystal Diamond (SCD)	Essential for minimizing background nuclear spin noise and maximizing NV coherence time.	Custom isotopic enrichment control (e.g., < 0.1% ¹³C or highly enriched > 99.99% ¹²C).
Optical Grade SCD Wafers	Necessary for efficient optical pumping, initialization, and readout of the NV e-spin.	High crystalline quality; low strain; low nitrogen/defect concentrations.
(111) Oriented Substrates (SCD)	Required for achieving perfectly aligned NV centers, crucial for realizing the predicted non-axial stability sites which depend on the NV axis symmetry.	Custom orientation selection, including (111) wafers up to 500µm thick.
PCD Diamond Plates	While SCD is preferred for fundamental quantum research, BDD or high-purity PCD can be utilized for analogous sensing applications requiring larger surface areas.	Plates up to 125mm in dimension; thicknesses up to 500µm.

Customization Potential for Quantum Engineers

6CCVD’s in-house engineering and manufacturing capabilities directly address the unique material requirements detailed in this advanced quantum research:

Isotopic Engineering: We offer precise control over the ¹³C concentration during MPCVD growth, allowing researchers to specify concentrations (e.g., 0.1% as used in the validation experiment, or below 50 ppm for maximal T2*).
Custom Dimensions and Thicknesses: SCD wafers/plates can be provided in thicknesses from 0.1µm up to 500µm, allowing flexibility for integration into quantum circuits or resonator cavities.
Ultra-Low Roughness Polishing: Achieving high-fidelity readout and surface preparation for metalization demands exceptional surface quality. 6CCVD guarantees Ra < 1nm for SCD, crucial for minimizing surface defects that can dephase near-surface NV centers.
Integrated Metalization Services: For device integration (e.g., microwave antennas used for ODMR/ENDOR, or contact pads), 6CCVD offers in-house metalization with materials including Au, Pt, Pd, Ti, W, and Cu.

Engineering Support & Consultation

6CCVD’s commitment extends beyond material supply. Our in-house PhD team provides technical consultation to assist researchers in selecting the optimal diamond material and specifications for demanding quantum projects. We specialize in tailoring material properties for applications such as room-temperature quantum memory, quantum metrology, and error correction codes based on NV-¹³C spin systems.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).

View Original Abstract

Single NV centers in diamond coupled by hyperfine interaction to neighboring\n13C nuclear spins are now widely used in the emerging quantum technologies as\nelements of quantum memory adjusted to NV center electron spin qubit. For\nnuclear spins with low flip-flop rate, single shot readout was demonstrated\nunder ambient conditions. Here we report on the systematic search of such\nstable NV-13C systems using density functional theory (DFT) to simulate\nhyperfine and spatial characteristics of all possible NV-13C complexes in the\nH-terminated cluster C510 [NV]-H252 hosting the NV center. Along with the\nexpected stable NV- axial 13C systems wherein the 13C nuclear spin is located\non the NV axis, we found for the first time new families of positions for the\n13C nuclear spin exhibiting negligible hyperfine-induced flipping rates due to\nnear-symmetric local spin density distribution. Spatially, these positions are\nlocated in the diamond bilayer passing through the vacancy of the NV center and\nbeing perpendicular to the NV axis. Analysis of available publications showed\nthat, apparently, some of the predicted non-axial near-stable systems NV-13C\nhave already been observed experimentally. A special experiment done on one of\nthese systems confirmed the prediction made\n

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Original Source

DOI: https://doi.org/10.1088/1367-2630/aaa910