Experimental and Theoretical Analysis of Noise Strength and Environmental Correlation Time for Ensembles of Nitrogen-Vacancy Centers in Diamond

At a Glance

Metadata	Details
Publication Date	2020-04-22
Journal	Journal of the Physical Society of Japan
Authors	kan hayashi, Yuichiro Matsuzaki, Takaki Ashida, Shinobu Onoda, Hiroshi Abe
Institutions	Kyoto University Institute for Chemical Research, National Institute for Materials Science
Citations	17
Analysis	Full AI Review Included

Technical Documentation & Analysis: NV Center Decoherence in Diamond

Reference Paper: Experimental and theoretical analysis of noise strength and environmental correlation time for ensembles of nitrogen-vacancy centers in diamond (Hayashi et al.)

Executive Summary

This research provides critical insights into optimizing Nitrogen-Vacancy (NV) center ensembles for high-performance quantum devices by systematically linking spin concentration to decoherence dynamics.

Core Achievement: Demonstrated a clear, systematic relationship between the total spin concentration (NV + P1 centers) and the decoherence behavior (Hahn echo decay curve).
Decay Crossover: Observed a crossover from non-exponential decay (low concentration) to exponential decay (high concentration), crucial for understanding entanglement sensor limitations.
Noise Quantification: Quantitatively showed that both the noise amplitude ($\lambda$) and the inverse environmental correlation time ($1/\tau_c$) exhibit a linear dependence on the total spin concentration.
Decoherence Mechanism: Confirmed that dipole interactions from non-resonant spins, primarily P1 centers (substitutional nitrogen), are the dominant noise source limiting coherence time (T₂).
Material Implications: The study highlights the necessity of precise control over nitrogen (P1) and NV concentrations, and the reduction of other impurities (like ¹³C and residual metals), to maximize T₂ for quantum sensing applications.
Methodology: Utilized HPHT diamond, 2-MeV electron irradiation, 1000 °C annealing, and optically detected magnetic resonance (ODMR) via the Hahn echo sequence.

Technical Specifications

The following hard data points were extracted from the experimental section and tables, detailing the material properties and measurement conditions.

Parameter	Value	Unit	Context
P1 Concentration Range	0.44 to 33.6	$\times 10^{17}$ /cm³	Substitutional Nitrogen Impurities (Noise Source)
NV Concentration Range	0.06 to 18.4	$\times 10^{17}$ /cm³	Active Quantum Centers
Total Spin Concentration	Linear Dependence	N/A	Correlates linearly with noise parameters ($\lambda$, $1/\tau_c$)
Electron Irradiation Energy	2	MeV	Used to create vacancies for NV formation
Irradiation Dose Range	0.7 to 100	$\times 10^{16}$ e/cm²	Varies across nine HPHT samples
Annealing Temperature	1000	°C	Post-irradiation treatment (1 hour in Ar gas)
Measurement Temperature	Room	°C	Hahn echo sequence performed
Excitation Laser Wavelength	532	nm	Green laser for ODMR initialization/readout
Excitation Laser Power	50	µW	Used with confocal microscope
Rabi Frequency ($\Omega$)	$2\pi \times 8.3$	MHz	Used for $\pi$ pulse generation
$\pi$ Pulse Duration	$\approx 60$	nsec	Microwave pulse length
Applied Magnetic Field (B)	$\approx 30$	mT	Applied along the <111> direction

Key Methodologies

The experiment involved precise material preparation and advanced quantum measurement techniques to correlate defect density with spin coherence.

Material Preparation: Nine HPHT diamond crystals containing native P1 centers were selected as starting material.
Vacancy Creation: Samples were irradiated with 2-MeV electrons at $745 \pm 10$ °C, with doses ranging from $0.7 \times 10^{16}$ to $100 \times 10^{16}$ e/cm², to generate vacancies.
NV Center Formation: Subsequent high-temperature annealing was performed at 1000 °C for 1 hour in an Argon (Ar) atmosphere to mobilize vacancies and form NV centers.
Surface Treatment: Samples were cleaned in a boiling acid mixture (1:1 sulfuric:nitric) to remove graphitic carbon and surface termination layers.
Concentration Analysis: P1 concentration was measured using Electron Paramagnetic Resonance (EPR). NV concentration was estimated by comparing fluorescence intensity to a known single NV center.
Decoherence Measurement: The Hahn echo pulse sequence ($\pi/2 - \tau - \pi - \tau - \pi/2$) was performed at room temperature using a 532-nm laser and microwave pulses to measure the coherence time (T₂).
Theoretical Modeling: Experimental decay curves were fitted using a stretched exponential function and a random classical Gaussian noise model to extract the noise amplitude ($\lambda$) and environmental correlation time ($\tau_c$).

6CCVD Solutions & Capabilities

The research confirms that maximizing NV center coherence time (T₂) requires stringent control over nitrogen concentration (P1 centers) and the elimination of extraneous spin baths (like ¹³C). 6CCVD’s expertise in high-purity MPCVD diamond growth directly addresses the limitations identified in the HPHT samples used in this study.

Applicable Materials for Quantum Sensing

To replicate or extend this research toward optimized quantum sensors, 6CCVD recommends the following materials, which offer superior purity and control compared to the HPHT samples used:

6CCVD Material Solution	Application Focus	Technical Advantage over HPHT
Optical Grade SCD (Single Crystal Diamond)	Baseline material for NV ensemble creation.	Inherently lower metallic and non-nitrogen impurities, maximizing intrinsic T₂.
Isotopically Pure SCD (99.99% ¹²C)	High-coherence quantum memory and sensing.	Eliminates the dominant ¹³C nuclear spin bath, suppressing unwanted oscillations and drastically extending T₂.
Custom Nitrogen-Doped SCD	Targeted NV ensemble density optimization.	Allows precise, in-situ control of P1 concentration during MPCVD growth, enabling systematic studies of the $\lambda$ and $\tau_c$ dependence identified in this paper.
Polycrystalline Diamond (PCD) Wafers	Scalable, large-area ensemble magnetometers.	Provides substrates up to 125mm in diameter for high-throughput sensor fabrication.

Customization Potential for Advanced Research

The systematic study of spin concentration requires highly tailored substrates. 6CCVD provides the necessary engineering capabilities to meet these demands:

Precise Defect Engineering: We provide SCD substrates with controlled, low nitrogen content, serving as a superior starting point for post-processing (irradiation/annealing) to create optimized NV ensembles.
Custom Dimensions and Thickness: While the paper used small samples, 6CCVD can supply SCD plates up to 10x10mm and PCD wafers up to 125mm, with thicknesses ranging from 0.1µm to 500µm, supporting both thin-film and bulk sensor designs.
Surface Preparation: We offer ultra-low roughness polishing (Ra < 1nm for SCD) essential for minimizing surface noise and maximizing the efficiency of optical readout (ODMR) systems.
Metalization Services: If the research requires integrated microwave circuitry or contacts (e.g., for applying the $\pi$ pulses or magnetic fields), 6CCVD offers internal metalization capabilities including Au, Pt, Pd, Ti, W, and Cu deposition.

Engineering Support

The linear dependence of noise parameters on spin concentration is crucial for developing next-generation quantum sensors. 6CCVD’s in-house PhD team specializes in material selection and optimization for similar NV-based Quantum Sensing and Quantum Information Processing projects. We assist researchers in defining the optimal nitrogen doping levels and isotopic purity required to achieve target T₂ coherence times.

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

View Original Abstract

We experimentally and theoretically investigate the Hahn echo decay curve for\nnitrogen vacancy centers in diamond with different spin concentrations. The\nHahn echo results show a non-exponential decay for low spin concentrations,\nwhile an exponential decay is dominant for high spin concentrations. By fitting\nthe decay curve with a theoretical model, we show that both the amplitude and\ncorrelation time of the environmental noise have a clear dependence on the spin\nconcentration. These results are essential for optimizing the NV center\nconcentration in high-performance quantum devices, particularly quantum\nsensors.\n

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Original Source

DOI: https://doi.org/10.7566/jpsj.89.054708