Algorithmic decomposition for efficient multiple nuclear spin detection in diamond

At a Glance

Metadata	Details
Publication Date	2020-09-10
Journal	Scientific Reports
Authors	Hyunseok Oh, Jiwon Yun, M. H. Abobeih, Kyung Hoon Jung, Kiho Kim
Institutions	QuTech, Seoul National University
Citations	4
Analysis	Full AI Review Included

Algorithmic Decomposition for Efficient Multiple Nuclear Spin Detection in Diamond: A 6CCVD Technical Analysis

This document analyzes the research paper “Algorithmic decomposition for efficient multiple nuclear spin detection in diamond” and outlines how 6CCVD’s specialized MPCVD diamond materials and engineering services can support and advance this critical research in quantum sensing and information processing.

Executive Summary

This paper presents a systematic, automated algorithmic method for characterizing multiple ¹³C nuclear spins weakly coupled to a Nitrogen-Vacancy (NV) center electron spin in diamond, a key step toward scalable quantum systems.

Core Achievement: Development of an automated algorithm to decompose complex Carr-Purcell-Meiboom-Gilbert (CPMG) dynamical decoupling spectra.
Functionality: The algorithm automatically identifies periodic coherence dips and accurately determines the parallel (A) and perpendicular (B) hyperfine interaction tensor components of individual nuclear spins.
Material Platform: Nitrogen-Vacancy (NV) centers in diamond, leveraging the long coherence times of the electron spin (S=1) and surrounding ¹³C nuclear spins (I=1/2).
Performance: Demonstrated detection of up to ten virtual nuclear spins with < 5% error, and successful re-analysis of experimental data detecting 14 distinct nuclear spins.
Resolution: Achieved a dip frequency resolution of approximately 2 kHz, with 80% confidence for hyperfine parameters in the range |A|: 5 kHz to 70 kHz and |B|: 15 kHz to 80 kHz.
Scalability: Provides a fast, general tool for analyzing complex spin structures, facilitating the scalability of NV center-based quantum devices.

Technical Specifications

The following hard data points were extracted from the methodology and results sections of the paper:

Parameter	Value	Unit	Context
Spin System	NV Center (S=1) / ¹³C Nuclear Spin (I=1/2)	N/A	Quantum register platform
Applied Magnetic Field (B₀)	400	G	Along the NV center axis
Pulse Sequence Type	CPMG	N/A	Dynamical decoupling sequence
Pulse Repetition Number (N)	32	N/A	Used for both virtual and experimental data
Pulse Duration ($\tau$) Range	0 to 50	µs	Varied with 5 ns interval
Hyperfine A Range (80% Confidence)	5 <	A	< 70
Hyperfine B Range (80% Confidence)	15 <	B	< 80
Dip Frequency Resolution	2	kHz	Achieved resolution for reliable distinction
Algorithm Error (Virtual Data)	< 5	%	Error in reconstructed CPMG signal
Algorithm Error (Hyperfine Parameters)	< 20	%	Error relative to reference values for reliable spins
Algorithm User Parameter: `threshold`	0.05	N/A	Minimum amplitude to distinguish noise and signal
Algorithm User Parameter: `M`	3	N/A	Number of additional layers of dips used

Key Methodologies

The automated algorithmic analysis of the CPMG nuclear spectra is executed in three sequential, automated stages:

Signal Decomposition into Gaussians:
- The CPMG dynamical decoupling signal is automatically divided into fragments, ensuring nominally only one coherence dip exists per fragment.
- Expectation-Maximization (EM) iterations are used to decompose each fragment into a combination of Gaussian functions.
- Gaussian outputs with amplitudes smaller than the user-defined threshold (0.05) are eliminated as noise.
Detection of Single Nuclear Spins (CPMG Line Fit Method):
- Coherence dip positions ($\Delta\tau$) are plotted as a function of the pulse repetition index ($k$), forming a fan diagram.
- A sequential process identifies sets of straight lines starting near the origin (k, $\Delta\tau$) = (0.5, 0), where each line represents a single nuclear spin.
- The slope of the fitted line ($\frac{d\tau}{dk}$) is used to calculate the initial estimate of the hyperfine interaction components A and B, based on the linear approximation of the resonance condition.
Fitting and Post Selection:
- The full-width-half-maximum (FWHM) of the grouped dips and the slope ($\frac{d\tau}{dk}$) are used as two constraints to determine the final (A, B) values.
- The FWHM is related to the Lorentzian envelope of the CPMG signal, providing a constraint on B.
- A MATLAB fit function is applied iteratively, using the initial A and B estimates, while applying a filter based on the root-mean-square error (RMSE) to prevent unphysical fitting due to interference from nearby dips.
- A Beam Search heuristic strategy is used for post-selection to find the optimal (A, B) pair configuration that best reconstructs the original CPMG signal.

6CCVD Solutions & Capabilities

The successful implementation and scaling of NV center-based quantum systems, as demonstrated in this paper, rely fundamentally on ultra-high-quality diamond materials. 6CCVD is uniquely positioned to supply the necessary MPCVD diamond substrates and engineering services required to replicate and extend this research.

Applicable Materials for NV Center Research

The long coherence times and low strain required for high-fidelity quantum control necessitate the use of Single Crystal Diamond (SCD) grown via Microwave Plasma Chemical Vapor Deposition (MPCVD).

6CCVD Material Solution	Specification & Relevance to Research
High-Purity SCD (Electronic Grade)	Essential for maximizing NV electron spin coherence (T₂). Low nitrogen content ([N] < 1 ppb) minimizes paramagnetic defects that cause decoherence.
Isotopically Engineered SCD	Critical for controlling the nuclear spin bath. We offer SCD with depleted ¹³C (e.g., < 0.1%) to maximize T₂* and T₂ coherence times, or enriched ¹³C (e.g., natural abundance or higher) for controlled spin bath studies, as utilized in this paper.
Low-Strain SCD Substrates	Low internal strain is vital for maintaining the spectral stability and homogeneity of the NV centers, ensuring sharp, detectable coherence dips required by the algorithmic analysis.
Custom Thickness SCD	SCD plates available from 0.1 µm up to 500 µm thickness, allowing researchers to optimize NV creation depth (e.g., via ion implantation) and integration into microwave structures.

Customization Potential for Quantum Devices

The complexity of NV center experiments often requires non-standard geometries and integrated components. 6CCVD provides comprehensive in-house customization capabilities:

Custom Dimensions and Shapes: We supply SCD and PCD plates up to 125 mm in diameter. Custom laser cutting services allow for precise shaping of substrates to fit specific cryogenic or microwave setups (e.g., creating micro-structures or waveguides).
Ultra-Low Roughness Polishing: Quantum experiments, especially those involving optical coupling to NV centers, demand pristine surfaces. 6CCVD guarantees Ra < 1 nm polishing for SCD, ensuring minimal scattering loss and high-quality NV formation near the surface.
Internal Metalization Services: While the paper focuses on signal processing, the NV platform requires microwave control. We offer internal metalization capabilities, including deposition of Ti, Pt, Au, Pd, W, and Cu layers, essential for fabricating microwave striplines and electrodes directly onto the diamond surface.

Engineering Support

6CCVD’s in-house team of PhD material scientists and quantum engineers specializes in optimizing diamond properties for quantum applications.

Material Selection Consultation: Our experts can assist researchers in selecting the optimal ¹³C concentration and nitrogen doping level required to replicate or extend this specific NV center-based nuclear spectroscopy project.
NV Creation Optimization: We provide guidance on substrate preparation (polishing, cleaning) to maximize the yield and coherence of near-surface NV centers, which are often used for sensing external spins.
Global Logistics: We ensure reliable, global shipping (DDU default, DDP available) of sensitive, high-value diamond materials directly to research facilities worldwide.

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

Tech Support

Original Source

DOI: https://doi.org/10.1038/s41598-020-71339-6