Relaxation of a dense ensemble of spins in diamond under a continuous microwave driving field

At a Glance

Metadata	Details
Publication Date	2021-08-11
Journal	Scientific Reports
Authors	Jeson Chen, Oliver Y. Chén, Huan‐Cheng Chang
Institutions	Feng Chia University, Institute of Atomic and Molecular Sciences, Academia Sinica
Citations	5
Analysis	Full AI Review Included

Technical Documentation & Analysis: NV⁻ Spin Relaxation in Diamond

This document analyzes the research paper “Relaxation of a dense ensemble of spins in diamond under a continuous microwave driving field” to provide technical specifications and highlight how 6CCVD’s advanced MPCVD diamond materials and customization capabilities can accelerate and extend this critical quantum research.

Executive Summary

Core Achievement: Detailed investigation and measurement of the baseline decay time ($T_b$) of dense Nitrogen-Vacancy (NV⁻) spin ensembles in diamond under continuous microwave (CW MW) driving.
Key Finding: The baseline decay time ($T_b$) decreases significantly (up to 50%) as the MW field strength (Rabi frequency, $\Omega_R$) increases, showing a Lorentzian-like dependence on MW detuning ($\delta$).
Material Limitation: The Type-Ib diamond used (150 ppm substitutional N, 10 ppm NV⁻) exhibited severely limited coherence times ($T_2 \approx 1.7$ µs), confirming that high defect density is the critical challenge for practical ensemble quantum applications.
Methodology: Utilized a home-built wide-field fluorescence imaging setup, 532-nm CW laser pumping, and MW delivery via a gold wire, analyzed using a double-stretched exponential fit derived from Bloch formalism.
6CCVD Value Proposition: 6CCVD specializes in ultra-high purity Single Crystal Diamond (SCD) and custom low-N Polycrystalline Diamond (PCD) substrates, directly addressing the material purity limitations required to maximize $T_1$ and $T_2$ coherence times for high-fidelity quantum metrology.
Customization Advantage: We offer integrated metalization (e.g., Ti/Pt/Au) directly on the diamond surface, enabling superior on-chip MW delivery and eliminating the field inhomogeneity issues encountered in the experiment.

Technical Specifications

The following table extracts key quantitative data and material parameters from the research paper.

Parameter	Value	Unit	Context
NV Center Density	~10	ppm	Used in the FMD microcrystal sample
Substitutional N Density	~150	ppm	Used in the Type-Ib diamond sample
Spin-Spin Relaxation Time ($T_2$)	1.7 ± 0.13	µs	Measured via Hahn echo technique
Spin-Lattice Relaxation Time ($T_1$)	1491 ± 257	µs	Measured via spin-lattice relaxation
Zero Field Splitting ($D$)	2.87	GHz	Transition frequency between $
Static Magnetic Field ($B_{		}$)	~6.6
Laser Wavelength	532	nm	Continuous-Wave (CW) optical pumping and probing
Laser Power Density	~1	kW/cm²	Used to minimize photoionization effects
Rabi Frequency ($\Omega_R/2\pi$)	3.44	MHz	Observed maximum Rabi nutation frequency
Baseline Decay Reduction	Up to 50	%	Decrease observed at high MW power ($\Omega_R/2\pi > 1$ MHz)
Inhomogeneous Broadening ($\Delta\omega_{fs}/2\pi$)	~7	MHz	Total width of ¹⁴N hyperfine structures
Sample Size	~100	µm	Diameter of the Fluorescent Microdiamond (FMD) crystal

Key Methodologies

The experiment focused on measuring the spin relaxation dynamics of dense NV⁻ ensembles under continuous MW driving using time-resolved photoluminescence (PL) detection.

Optical Initialization: Electron spins were polarized to the $|m_s = 0\rangle$ sublevel using a 532-nm CW laser pulse (300 µs duration).
MW Driving: Continuous-Wave Microwave (CW MW) radiation was applied during a variable delay time $t$ via a gold wire positioned 5 µm from the diamond surface.
Optical Readout: The spin state was read out using a short laser pulse (0.5 µs duration), detecting the difference in PL intensity between $|m_s = 0\rangle$ and $|m_s = \pm 1\rangle$ states.
Signal Normalization: Signals were normalized by dividing the signal frame (with variable delay $t$) by a reference frame (fixed 2 µs delay) to correct for laser intensity fluctuations and low-frequency noise.
Data Fitting: The resulting PL decay traces were fitted using a double-stretched exponential function (Eq. 3) to isolate the slow, millisecond-scale baseline decay component ($T_b$) from the fast, microsecond-scale oscillatory amplitude decay component.
Relaxation Time Measurement: $T_1$ and $T_2$ were measured separately using standard techniques (spin-lattice relaxation and Hahn echo, respectively) to provide reference values for simulation.

6CCVD Solutions & Capabilities

The research successfully characterized spin relaxation in dense NV⁻ ensembles, but the results were fundamentally limited by the short coherence time ($T_2 \approx 1.7$ µs) inherent to the high nitrogen concentration (150 ppm N) Type-Ib diamond used. 6CCVD provides the advanced MPCVD materials necessary to overcome these limitations and push the boundaries of quantum metrology.

Applicable Materials for Replication and Extension

To achieve the long coherence times required for practical, high-fidelity quantum applications, researchers must transition from high-N Type-Ib microcrystals to ultra-pure MPCVD diamond.

Research Requirement	6CCVD Material Solution	Key Benefit
High Coherence ($T_2$ >> 1.7 µs)	Optical Grade Single Crystal Diamond (SCD)	Ultra-low nitrogen concentration (sub-ppb N) minimizes spin bath noise, maximizing $T_2$ and $T_1$ coherence times.
Large-Scale Sensing	Low-N Polycrystalline Diamond (PCD)	Wafers up to 125mm diameter, providing large detection volumes for ensemble sensing while maintaining superior purity compared to Type-Ib.
High-Density Sensing (BDD)	Boron-Doped Diamond (BDD)	Available in SCD or PCD formats for electrochemical and high-sensitivity applications requiring conductive diamond properties.

Customization Potential for Advanced Experiments

The experimental setup relied on an external gold wire for MW delivery, which contributed to inhomogeneous broadening ($\Omega_R$ variation) and complicated the analysis. 6CCVD offers integrated solutions to enhance experimental control and fidelity:

Integrated Metalization: 6CCVD offers in-house deposition of thin-film metals (Au, Pt, Pd, Ti, W, Cu) directly onto the diamond surface. This capability allows researchers to pattern precise on-chip MW waveguides (e.g., coplanar waveguides or strip lines) using standard lithography, ensuring highly homogeneous $\Omega_R$ fields across the NV ensemble.
Custom Dimensions and Thickness: While the paper used a 100 µm microcrystal, 6CCVD can supply SCD plates with thicknesses ranging from 0.1 µm to 500 µm, or robust substrates up to 10 mm thick, tailored to specific optical or mechanical mounting requirements.
Ultra-Smooth Surfaces: Our SCD materials are polished to an atomic level (Ra < 1 nm), minimizing surface defects that can act as charge traps or decoherence sources, crucial for maintaining spin stability near the surface.

Engineering Support

The successful analysis of this research required complex theoretical modeling based on the Bloch formalism, accounting for inhomogeneous broadening and coupled spin-charge dynamics. 6CCVD’s in-house PhD material science team provides expert consultation to help researchers:

Optimize NV Density: We assist in selecting the optimal nitrogen concentration and subsequent NV creation parameters (e.g., electron irradiation and annealing recipes) to balance signal strength (high NV density) against coherence time (low N background).
Material Selection: Guidance on choosing between SCD (for ultimate coherence) and PCD (for large-area homogeneity) based on the specific quantum metrology or sensing application requirements.

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/s41598-021-95722-z