Double-Quantum Spin-Relaxation Limits to Coherence of Near-Surface Nitrogen-Vacancy Centers

At a Glance

Metadata	Details
Publication Date	2017-05-09
Journal	Physical Review Letters
Authors	Bryan Myers, Amila Ariyaratne, Ania C. Bleszynski Jayich
Institutions	University of California, Santa Barbara
Citations	120
Analysis	Full AI Review Included

Technical Documentation & Analysis: Double-Quantum Spin-Relaxation Limits in Near-Surface NV Centers

Executive Summary

This paper introduces a critical advancement in understanding NV (Nitrogen-Vacancy) center decoherence, specifically highlighting the dominant role of surface-related noise in shallow NV applications.

Core Finding: The coherence limit ($T_{2} \le 2T_{1}$) for near-surface NVs is primarily defined by Double-Quantum (DQ) spin relaxation ($\gamma$), rather than the traditional Single-Quantum (SQ) relaxation ($\Omega$).
Decoherence Source: DQ relaxation ($\gamma$) is dominated by electric field noise originating at the diamond surface, contrasting with previous work often focused solely on magnetic noise.
Methodological Breakthrough: A novel noise spectroscopy technique is demonstrated, combining SQ dephasing (CPMG-N) and DQ relaxometry, enabling quantitative differentiation between surface electric and magnetic field noise spectra over a broad frequency range.
Material Requirement: Achieving long coherence times requires ultra-high purity, isotopically enriched ¹²C MPCVD Single-Crystal Diamond (SCD) with precise layer control (40-50 nm) and ultra-low surface roughness (Ra ~ 160 pm).
Performance Metrics: Experimental data showed that accounting for DQ relaxation leads to a true $T_{1}$ (0.69 ms, NVA1), which is ~4 times shorter than the traditional $T_{1}^{(0)}$ (2.90 ms) that neglects surface effects. The measured $T_{2}$ reached 60(20)% of the theoretical $2T_{1}$ limit.
Fabrication Complexity: Replication requires sophisticated processing, including low-energy ¹⁴N ion implantation, high-temperature vacuum annealing, and nanoscale fabrication of diamond nanopillars and custom Ti/Au metalization.

Technical Specifications

Data extracted primarily from NVA1 at low applied magnetic field ($\omega_{\pm 1}/2\pi = 37.1$ MHz).

Parameter	Value	Unit	Context
Material Base	SCD	N/A	(001) Single-Crystal Diamond (E6 Grade Substrate)
CVD Layer Isotopic Purity	99.99% ¹²C	%	Grown via MPCVD
CVD Layer Thickness	40-50	nm	Ultra-thin layer for shallow NV centers
Surface Roughness (Ra)	160	pm	Required post-polishing quality (Ra < 1 nm)
N Ion Implantation Energy	4.0	keV	¹⁴N implantation for ~7 nm NV depth
N Ion Dose (Density)	5.2 x 10¹⁰	cm^-2	Target density for single-NV applications
Annealing Conditions	850	°C	High-vacuum environment, 2.5 hours
Double-Quantum ($\gamma$) Rate (NVA1)	1.11(5)	kHz	Dominated by surface electric field noise
Single-Quantum ($\Omega$) Rate (NVA1)	0.115(4)	kHz	Magnetic field noise contribution
Full $T_{1}$ Relaxation Time (NVA1)	0.69(7)	ms	True $T_{1} = (3\Omega + \gamma)^{-1}$
Maximum $T_{2}$ Coherence Time (NVA1, CPMG-512)	0.41(4)	ms	Coherence limited by spectral density
Maximum $T_{2}/T_{1}$ Ratio Achieved (NVA1)	60(20)	%	Achieving the $T_{2} \le 2T_{1}$ limit
NV Center Depth	~7	nm	Nanometers from the diamond surface
Metalization Layers	Ti/Au (6 nm/350 nm)	N/A	Microwave stripline fabrication

Key Methodologies

The following list outlines the critical steps and parameters used in the diamond material preparation and quantum measurements described in the research.

Substrate Preparation: Electronic grade SCD substrates (2 x 2 x 0.5 mm³) were sliced, polished to 150 µm thickness, and etched using ArCl₂ plasma (ICP 500 W, bias 200 W) to mitigate subsurface damage, resulting in Ra ~ 160 pm.
MPCVD Growth: A 40-50 nm thick, isotopically purified ¹²C (99.99%) diamond layer was grown via Plasma-Enhanced Chemical Vapor Deposition (PECVD) at 800 °C, 750 W.
NV Center Formation: Shallow NV centers were created using 4 keV ¹⁴N ion implantation (5.2 x 10¹⁰ cm^-2 dose), followed by high-vacuum annealing at 850 °C for 2.5 hours.
Nanofabrication: Diamond nanopillars (400 nm diameter, 500 nm height) were patterned using e-beam lithography and subsequent O₂ plasma etching to enhance Photoluminescence (PL) collection efficiency, minimizing long averaging times.
Microwave Control: Standard photolithography was used to pattern Ti/Au (6 nm/350 nm) microstrip waveguides for coherent $\left|0\right> \leftrightarrow \left|\pm 1\right>$ spin rotations (spin inversion $\pi_{0,\pm 1}$ pulses).
Quantum Measurement: Experiments utilized a room-temperature confocal microscope setup to perform:
- Single-Quantum (SQ) coherence measurements via dynamical decoupling (CPMG-N).
- DQ relaxometry, using two-tone microwave measurements to extract the relaxation rate $\gamma$ between $\left|+1\right>$ and $\left|-1\right>$ spin states.
Noise Spectroscopy: The measured rates ($\Omega$ and $\gamma$) were combined and deconvolved to quantitatively map the spectral character of surface electric and magnetic field noise components.

6CCVD Solutions & Capabilities

This research demonstrates the necessity of high-precision materials engineering for advancing near-surface quantum applications. 6CCVD is uniquely positioned to supply the demanding SCD products required to replicate and extend this foundational work.

Applicable Materials

To achieve the stringent purity, thickness control, and surface quality required for high-coherence, shallow NV centers, 6CCVD recommends:

Optical Grade SCD: SCD wafers serving as the electronic-grade substrate base, polished to achieve Ra < 1 nm, essential for minimizing surface noise introduced during polishing.
Isotopically Enriched ¹²C SCD Layers: We provide custom MPCVD growth of ultra-thin, high-purity ¹²C diamond layers (99.99% purity or higher, matching or exceeding the paper’s specification) in the 40 nm - 500 µm range, perfect for low-energy ion implantation studies.
Custom Thickness Control: We offer precise thickness control down to 0.1 µm (100 nm) for PCD and SCD, allowing researchers to explore NV layer thickness dependence on decoherence as suggested by the study.

Customization Potential

The success of this research relied heavily on sophisticated post-processing capabilities that are standard offerings at 6CCVD:

Research Requirement	6CCVD Capability	Application/Value Proposition
Low-Decoherence Substrates	SCD Wafers up to 125 mm	High-purity MPCVD SCD base material for scalable quantum integration.
Ultra-Precision Polishing	Ra < 1 nm (SCD)	Essential for mitigating surface-related electric field noise identified as the $T_{1}$ limiting factor.
Custom Metalization	Au, Pt, Pd, Ti, W, Cu	In-house deposition of Ti/Au (6 nm/350 nm specified in paper) or alternative metal stacks for microwave striplines and integrated quantum circuits.
Nanofabrication & Integration	Custom Laser Cutting & Shaping	While nanopillar etching is a specialized tool, 6CCVD provides precision laser cutting and shaping services to produce custom dies and integrated waveguide structures up to 125mm.
NV Depth Control	CVD layer control (0.1 µm - 500 µm)	Providing the optimal, highly enriched ¹²C growth layer necessary for precise, low-energy ion implantation (4 keV) and subsequent shallow NV formation (7 nm depth).

Engineering Support

The differentiation between electric and magnetic surface noise is critical for designing next-generation quantum sensors and solid-state defects ($S > 1/2$).

6CCVD’s in-house PhD technical engineering team specializes in diamond material optimization for quantum applications. We can provide consultation on:

Material Selection: Choosing the correct isotopic purity (e.g., ¹²C enrichment) and crystal orientation ((001) as used in this study) to minimize bulk decoherence channels.
Surface Preparation: Advising on optimal polishing (Ra requirements) and pre/post-CVD etching protocols (like ArCl₂ plasma) to maintain pristine surface quality and minimize structural defects that contribute to electric field noise.
Custom Design: Assisting with the specification of metalization thickness and patterning geometry necessary for integrating microwave components and magnetic field coils on the diamond chip.

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

View Original Abstract

We probe the relaxation dynamics of the full three-level spin system of near-surface nitrogen-vacancy (NV) centers in diamond to define a T_{1} relaxation time that sets the T_{2}≤2T_{1} coherence limit of the NV’s subset qubit superpositions. We find that double-quantum spin relaxation via electric field noise dominates T_{1} of near-surface NVs at low applied magnetic fields. Furthermore, we differentiate 1/f^{α} spectra of electric and magnetic field noise using a novel noise-spectroscopy technique, with broad applications in probing surface-induced decoherence at material interfaces.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevlett.118.197201