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	Center for Astrophysics Harvard & Smithsonian, Harvard University
Citations	189
Analysis	Full AI Review Included

Technical Documentation & Analysis: NV Ensemble Decoherence in MPCVD Diamond

Reference: Bauch et al., “Decoherence of dipolar spin ensembles in diamond,” arXiv:1904.08763v1 (2019).

Executive Summary

This research provides critical scaling laws for the decoherence of Nitrogen-Vacancy (NV) electronic spin ensembles in diamond, directly linking quantum performance metrics ($T_2$ and $T_2^*$) to material purity.

Core Finding: Both the spin-echo coherence time ($T_2$) and the free induction decay time ($T_2^*$) exhibit an inverse-linear dependence on the substitutional nitrogen concentration ([N]) in the range of 0.5 ppm to 300 ppm.
Limiting Factor: Decoherence is dominated by dipolar interactions with the paramagnetic substitutional nitrogen impurities (P1 centers), confirming that material purity is the primary constraint on ensemble quantum performance.
Coherence Rates: The nitrogen-dominated decoherence rate ($B_{NV-N}$) for $T_2$ was quantified as $2\pi \times (1.0 \pm 0.1)$ kHz/ppm, while the dephasing rate ($A_{NV-N}$) for $T_2^*$ was $2\pi \times (16 \pm 1.5)$ kHz/ppm.
Saturation Limit: $T_2$ saturates at approximately $700$ µs for ultra-low [N] (< 0.5 ppm), indicating that achieving millisecond coherence requires diamond material with [N] in the parts-per-billion (ppb) range and potentially low $^{13}$C content.
Decay Shapes: $T_2$ decay follows a stretched exponential ($p \approx 1.37$), while $T_2^*$ decay is a simple exponential ($p = 1$), consistent with ensemble averaging over many individual NV centers.
Material Requirement: Replicating or extending this work requires ultra-high purity, isotopically controlled Single Crystal Diamond (SCD) grown via MPCVD, a core capability of 6CCVD.

Technical Specifications

The following hard data points were extracted from the experimental results, defining the performance limits of NV ensembles based on nitrogen concentration.

Parameter	Value	Unit	Context
Nitrogen Concentration Range ([N])	10 ppb - 300 ppm	N/A	Range of samples studied (CVD and HPHT)
$T_2$ Saturation Limit	$\approx 700$	µs	Observed for [N] $\le 0.5$ ppm
$T_{2,other}$ (Decoherence Floor)	$694 \pm 82$	µs	Decoherence independent of nitrogen
$T_2$ Rate Constant ($B_{NV-N}$)	$160 \pm 12$	µs $\cdot$ ppm	Inverse-linear scaling factor for $T_2$
$T_2^*$ Rate Constant ($A_{NV-N}$)	$9.6 \pm 0.9$	µs $\cdot$ ppm	Inverse-linear scaling factor for $T_2^*$
$T_2$ Decay Parameter ($p$)	$1.37 \pm 0.23$	N/A	Stretched exponential decay envelope
$T_2^*$ Decay Parameter ($p$)	$1.0$	N/A	Simple exponential decay envelope
Carbon Isotope Purity ($^{13}$C)	$\le 0.05$	%	Used in isotopically enriched samples (”$^{12}$C-samples”)
Static Magnetic Field ($B_0$)	2 - 30	mT	Applied along [111] crystal direction
Optical Initialization Wavelength	532	nm	Used for NV spin initialization and readout

Key Methodologies

The study relied on precise material engineering and advanced quantum measurement techniques to isolate the effects of the nitrogen spin bath.

Material Growth: Samples were sourced from both Chemical Vapor Deposition (CVD) for low [N] ($\le 100$ ppm) and High-Pressure High-Temperature (HPHT) for high [N] ($\ge 100$ ppm). Thin nitrogen-doped layers ($\le 100$ µm) were grown on Ib or IIa substrates.
Concentration Measurement: Total nitrogen concentration ([N]) was determined using multiple methods, including Secondary Ion Mass Spectroscopy (SIMS) and Fourier-Transformed Infrared Spectroscopy (FTIR).
Isotopic Control: Both natural abundance ($1.1%$ $^{13}$C) and isotopically enriched ($\le 0.05%$ $^{13}$C) diamond samples were used to isolate nitrogen-related decoherence from nuclear spin bath effects.
Quantum Measurement: Free Induction Decay (FID, Ramsey sequence) was used to measure $T_2^*$, and Spin Echo pulse sequences were used to measure $T_2$.
NV Isolation: Experiments were conducted in the regime where the NV concentration ([NV]) was much less than the nitrogen concentration ([N]) to ensure that decoherence was dominated by P1 centers, not NV-NV interactions.
Dephasing Mitigation: $T_2^*$ measurements were performed in the NV double quantum basis ($\vert -1 \rangle, \vert +1 \rangle$) to mitigate contributions from crystal strain fields and temperature fluctuations.

6CCVD Solutions & Capabilities

This research confirms that achieving long coherence times ($T_2$ and $T_2^*$) for NV ensemble quantum applications is fundamentally a material science challenge, requiring ultra-low nitrogen concentration and precise isotopic control. 6CCVD is uniquely positioned to supply the custom MPCVD diamond required to push coherence times beyond the limits reported in this study.

Applicable Materials

To replicate and extend the millisecond coherence goals implied by this research, 6CCVD recommends the following materials:

6CCVD Material Grade	Key Specification	Application Relevance
High-Purity SCD	[N] < 1 ppb (Intrinsic)	Essential for minimizing $B_{NV-N}$ and maximizing $T_2$ and $T_2^*$ beyond the 700 µs limit.
Isotopically Purified SCD	$^{13}$C $\le 0.05%$	Eliminates the $^{13}$C nuclear spin bath, which becomes the dominant decoherence mechanism when [N] is minimized.
Custom N-Doped SCD	[N] precisely controlled (ppb to ppm)	Ideal for researchers needing to systematically study the $T_2$ vs. [N] scaling laws or engineer specific NV/P1 ratios.
Optical Grade SCD	Ra < 1 nm Polishing	Required for high-fidelity optical initialization and readout (532 nm laser) used in the experiments.

Customization Potential

The paper utilized thin layers and bulk plates, often requiring precise geometry and surface preparation for integration into quantum devices. 6CCVD provides comprehensive customization services:

Custom Dimensions: We supply plates and wafers up to 125 mm (PCD) and SCD plates up to 500 µm thick, with substrates available up to 10 mm, accommodating both thin-film and bulk sensing architectures.
Precision Polishing: We guarantee ultra-smooth surfaces critical for high-quality optical access, offering Ra < 1 nm for SCD and Ra < 5 nm for inch-size PCD.
Metalization Services: While the paper focused on material properties, quantum devices often require integrated microwave delivery structures. 6CCVD offers in-house metalization using Au, Pt, Pd, Ti, W, and Cu for creating coplanar waveguides (CPWs) or striplines directly on the diamond surface.
Global Logistics: We ensure reliable, global shipping (DDU default, DDP available) for time-sensitive quantum research projects.

Engineering Support

The relationship between [N] concentration, growth method (CVD vs. HPHT), and resulting NV/P1 ratios is complex. 6CCVD’s in-house PhD team specializes in tailoring MPCVD growth recipes to achieve specific defect concentrations and isotopic purities required for NV Ensemble Quantum Sensing and Computing projects. We assist clients in defining the optimal material specifications to maximize coherence times for their specific application.

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

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