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	National Institutes for Quantum and Radiological Science and Technology, National Institute of Advanced Industrial Science and Technology
Citations	17
Analysis	Full AI Review Included

Executive Summary

This study provides a systematic experimental and theoretical analysis of decoherence in ensembles of Nitrogen-Vacancy (NV) centers in diamond, focusing on the relationship between spin concentration and coherence time (T₂).

Core Finding (Decay Crossover): The Hahn echo decay curve exhibits a clear crossover behavior: non-exponential decay dominates at low spin concentrations, while exponential decay is dominant at high spin concentrations.
Quantitative Relationship: Both the noise amplitude (λ) and the inverse environmental correlation time (1/t_c) of the electron spin bath show an almost linear dependence on the total spin concentration (NV center concentration plus P1 center concentration).
Decoherence Mechanism: The crossover is attributed to the change in the environmental noise characteristics (amplitude and correlation time) driven by the density of paramagnetic impurities (P1 centers and other NV centers).
Modeling Success: A theoretical model based on random classical Gaussian noise successfully fits the Hahn echo decay curves across the entire range of spin concentrations tested.
Engineering Relevance: These results are crucial for optimizing NV center concentration in diamond to maximize coherence time and performance, particularly for high-sensitivity quantum sensors and entanglement-enhanced devices (which require non-exponential decay behavior).
Noise Source Identification: Dipole interactions from nitrogen paramagnetic impurities (P1 centers) are confirmed as a dominant noise source for spin dephasing in high-density ensembles.

Technical Specifications

Parameter	Value	Unit	Context
NV Center Type	Spin 1	N/A	Electronic ground state.
Transition Frequency	~2.87	GHz	Electronic ground state (m_s = 0 to m_s = ±1).
Gyromagnetic Ratio (γ)	28	MHz/mT	Electron spin.
Magnetic Field (B)	~30	mT	Applied along the <111> direction for Hahn echo.
Rabi Frequency (Ω)	2π x 8.3	MHz	Used for π pulse duration (~60 nsec).
Laser Wavelength	532	nm	Used for optical initialization and readout.
Laser Power (Measurement)	50	µW	Used during Hahn echo sequence.
Detection Volume	0.04	µm³	Confocal microscope measurement volume.
Annealing Temperature	1000	°C	Post-irradiation annealing (1 hour in Ar gas).
Irradiation Temperature	745 ± 10	°C	2-MeV electron irradiation for NV creation.
Max P1 Concentration (No. 1)	33.6 x 10¹⁷	/cm³	Highest concentration sample.
Max NV Concentration (No. 1)	18.4 x 10¹⁷	/cm³	Highest concentration sample.
Max Electron Irradiation Dose	100 x 10¹⁶	e/cm²	Used for samples No. 1, 3, 4.
Demonstrated Sensitivity	0.9	pT/Hz^1/2	Achieved with 1.4 x 10¹¹ NV centers.
Optimal Theoretical Sensitivity	~250	aT/√Hz/cm^2/3	Theoretical limit for NV magnetometers.

Key Methodologies

The study involved the synthesis, preparation, and characterization of nine HPHT diamond samples, followed by systematic Hahn echo measurements.

Diamond Synthesis:
- Nine diamond crystals containing substitutional nitrogen (P1 centers) were synthesized using High-Pressure High-Temperature (HPHT) processes.
NV Center Creation:
- NV centers were created via 2-MeV electron irradiation at various doses (ranging from 0.7 x 10¹⁶ to 100 x 10¹⁶ e/cm²).
- Irradiation was performed at 745 ± 10 °C.
- Subsequent annealing was performed at 1000 °C for 1 hour in Ar gas.
Surface Cleaning:
- After annealing, diamonds were cleaned in a boiling acid mixture (1:1 sulfuric acid, nitric acid) to remove graphitic carbon and oxygen termination from the surface.
Concentration Measurement:
- P1 Concentration: Evaluated using Electron Paramagnetic Resonance (EPR) spectroscopy at room temperature.
- NV Concentration: Estimated by comparing the fluorescent intensity of the samples with that of a single NV center, using a lab-built confocal microscope (532-nm laser).
Hahn Echo Measurement:
- The Hahn echo sequence (π/2 - τ/2 - π - τ/2 - π/2) was performed at room temperature.
- Green laser pulses (532 nm, 50 µW) were used for initialization and readout.
- Microwave pulses were applied via a copper wire, achieving a Rabi frequency of 2π x 8.3 MHz.
- A permanent magnet applied a magnetic field (~30 mT) along the <111> direction to separate revival peaks from the main decay curve.
Data Analysis and Modeling:
- Initial T₂ estimation was performed using a simple stretched exponential function (exp(-(τ/T₂)ⁿ)).
- A more detailed fit of the Hahn echo decay envelope was performed using a random classical Gaussian noise model (Eq. 10/11) to extract the noise amplitude (λ) and environmental correlation time (t_c).

Commercial Applications

The findings regarding the control of decoherence through spin concentration are critical for the development and optimization of high-performance quantum devices based on NV centers in diamond.

Quantum Sensing and Metrology:
- High-Sensitivity Magnetometers: Optimizing NV concentration is essential for achieving the best balance between signal strength (more NV centers) and coherence time (less noise/decoherence), directly impacting sensitivity (pT/Hz^1/2).
- Nano-NMR/ESR: Enabling nanoscale magnetic resonance spectroscopy for chemical and biological analysis.
Quantum Information Processing (QIP):
- Quantum Memory: NV centers are promising candidates for long-lived quantum memory, requiring maximized coherence times.
- Distributed Quantum Computation: Utilizing NV ensembles for robust quantum communication links.
Entanglement-Enhanced Sensors:
- The ability to control the decay profile (crossover from exponential to non-exponential) is vital, as entanglement sensors are theoretically more effective only when the decoherence behavior is non-exponential.
Material Optimization:
- The linear relationship between noise parameters (λ, 1/t_c) and spin concentration provides a quantitative guide for diamond material engineers to tailor NV and P1 concentrations for specific application requirements (e.g., high-density sensing vs. long-coherence memory).

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

Tech Support

Original Source

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