Decoherence of ensembles of nitrogen-vacancy centers in diamond

At a Glance

Metadata	Details
Publication Date	2020-10-23
Journal	Physical review. B./Physical review. B
Authors	Erik Bauch, Swati Singh, Junghyun Lee, Connor Hart, Jennifer M. Schloss
Institutions	Korea Institute of Science & Technology Information, Harvard University
Citations	189
Analysis	Full AI Review Included

Executive Summary

This research provides a comprehensive experimental and theoretical analysis of electronic spin decoherence in Nitrogen Vacancy (NV) center ensembles in diamond, specifically focusing on the limiting effects of the substitutional nitrogen (P1) spin bath.

Core Achievement: Quantified the degradation of NV ensemble spin coherence times (T₂ and T₂*) across four orders of magnitude of nitrogen concentration ([N]), ranging from 0.01 to 300 ppm.
Key Scaling Law: Both T₂ (spin echo) and T₂* (free induction decay) exhibit a characteristic inverse-linear scaling with nitrogen concentration [N] in the high-density regime, confirming that P1 centers dominate decoherence.
T₂ Performance: The nitrogen-limited T₂ scales inversely with [N] at a rate of approximately 160 µs·ppm. The maximum observed T₂ saturates at about 700 µs in low-[N] samples.
T₂ Performance:* The nitrogen-limited T₂* scales inversely with [N] at a rate of approximately 9.6 µs·ppm.
Decay Modeling: The observed non-integer decay shapes for the NV ensemble (T₂ exponent p ≈ 1.37; T₂* exponent p = 1) are successfully explained by statistical ensemble averaging, consistent with the nitrogen bath dynamics modeled as an Orenstein-Uhlenbeck stochastic process.
Engineering Impact: The established scaling laws allow for rough calibration of bulk substitutional nitrogen concentrations using NV coherence measurements, critical for material quality control in quantum device fabrication.

Technical Specifications

Parameter	Value	Unit	Context
Nitrogen Concentration Range ([N])	0.01 to 300	ppm	Range of 25 diamond samples studied
¹³C Abundance (Natural)	1.1	%	Used for T₂ measurements
¹²C Abundance (Enriched)	≤ 0.05	%	Used for T₂* measurements (to mitigate ¹³C effects)
NV T₂ Inverse Scaling (1/B_NV-N)	160 ± 12	µs·ppm	Coherence time per unit nitrogen density
NV T₂ Saturation Limit (T_2,other)	694 ± 82	µs	Low [N] limit (independent of nitrogen)
NV T₂* Inverse Scaling (1/A_NV-N)	9.6 ± 0.9	µs·ppm	Dephasing time per unit nitrogen density
NV T₂ / T₂* Ratio	~16	unitless	Independent of [N] across the measured range
Spin Echo Decay Exponent (p)	1.37 ± 0.23	unitless	NV ensemble average (non-integer decay)
FID Decay Exponent (p)	1	unitless	NV ensemble average (simple exponential decay)
Applied Static Magnetic Field (B₀)	2 to 30	mT	Used to lift NV ground state degeneracy
Laser Wavelength	532	nm	Used for optical initialization and readout

Key Methodologies

Sample Sourcing and Characterization:
- Diamond crystals were sourced from Element Six and Apollo Diamond.
- Samples included bulk plates and thin layers (≤ 100 µm) grown via Chemical Vapor Deposition (CVD) for low [N] (≤ 100 ppm) and High-Pressure High-Temperature (HPHT) for high [N] (≥ 100 ppm).
- Total nitrogen concentration [N] was determined using Secondary Ion Mass Spectroscopy (SIMS), Fourier-Transformed Infrared Spectroscopy (FTIR), and manufacturer estimates.
Experimental Setup:
- NV spin measurements were performed using confocal or wide field microscopy.
- A static magnetic field (B₀) was applied along a [111] crystal direction (misalignment ≤ 3°) to select a single NV orientation and lift the |±1> degeneracy.
Spin Control and Measurement:
- Initialization/Readout: 532 nm laser light was used for optical initialization and readout of the NV spin polarization.
- Coherent Control: Pulsed microwaves were applied resonant with the |0> ↔ |±1> transitions.
- T₂ Measurement (FID/Ramsey):* Performed on isotopically enriched ¹²C samples ([¹³C] ≤ 0.05%) to isolate nitrogen effects. Measurements were conducted in the NV double quantum basis ({-1, +1}) to mitigate strain and temperature fluctuations.
- T₂ Measurement (Spin Echo): Performed on both ¹³C and ¹²C samples. Bias fields were adjusted to separate the overall decay envelope from ¹³C Larmor precession modulation.
Data Analysis and Modeling:
- Decay envelopes were fitted to the stretched exponential form C₀ exp[-(t/T)^p] to extract coherence times (T₂, T₂*) and the exponent p.
- The nitrogen-dominated decoherence rate (1/T) was fitted to an inverse-linear model: 1/T([N]) = B · [N] + 1/T_other.
- Theoretical modeling utilized an analytic model based on the Orenstein-Uhlenbeck stochastic process, supported by numerical simulations of 10⁴ spin bath configurations, to describe the ensemble-averaged decay shapes.

Commercial Applications

This research is foundational for optimizing diamond materials used in advanced quantum technologies:

Quantum Sensing and Metrology: Directly informs the design and material requirements for high-performance NV-ensemble-based quantum sensors (e.g., magnetometers, electrometers, and gyroscopes) where maximizing T₂ is critical for sensitivity.
Diamond Material Engineering: Provides a quantitative metric (T₂ and T₂* scaling) for assessing the quality and concentration of paramagnetic substitutional nitrogen (P1 centers), which are the primary decoherence source in high-density NV diamond. This enables better quality control for CVD and HPHT diamond growth.
Solid-State Quantum Computing: Relevant for developing robust solid-state spin platforms where NV centers are used as qubits or quantum memories, requiring precise control over the surrounding spin bath dynamics to achieve long coherence times.
Quantum Device Development: The ability to predict coherence times based on nitrogen concentration allows engineers to select or specify diamond substrates tailored for specific applications (e.g., high [N] for high-density sensing arrays, low [N] for maximum coherence).

View Original Abstract

We present a combined theoretical and experimental study of solid-state spin\ndecoherence in an electronic spin bath, focusing specifically on ensembles of\nnitrogen vacancy (NV) color centers in diamond and the associated\nsubstitutional nitrogen spin bath. We perform measurements of NV spin free\ninduction decay times $T_2^$ and spin-echo coherence times $T_2$ in 25 diamond\nsamples with nitrogen concentrations [N] ranging from 0.01 to 300\,ppm. We\nintroduce a microscopic model and perform numerical simulations to\nquantitatively explain the degradation of both $T_2^$ and $T_2$ over four\norders of magnitude in [N]. Our results resolve a long-standing discrepancy\nobserved in NV $T_2$ experiments, enabling us to describe NV ensemble spin\ncoherence decay shapes as emerging consistently from the contribution of many\nindividual NV.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.102.134210

References

2018 - in Proceedings of the IEEE/ION Position, Location, and Navigation Symposium