State-selective intersystem crossing in nitrogen-vacancy centers

At a Glance

Metadata	Details
Publication Date	2015-04-08
Journal	Physical Review B
Authors	Michael Goldman, Marcus W. Doherty, Alp Sipahigil, Norman Y. Yao, Steven Bennett
Institutions	Harvard University, Australian National University
Citations	141
Analysis	Full AI Review Included

Technical Analysis and Documentation: State-Selective Intersystem Crossing in Nitrogen-Vacancy Centers

This document analyzes the research paper “State-selective intersystem crossing in nitrogen-vacancy centers” (arXiv:1412.4865v2) to provide technical specifications and material recommendations, leveraging 6CCVD’s expertise in MPCVD diamond for quantum applications.

Executive Summary

The following points summarize the core findings of the research and the resulting material requirements for advanced quantum applications:

Core Mechanism Modeled: A microscopic model of the state-selective Intersystem Crossing (ISC) mechanism in the Nitrogen-Vacancy (NV) center excited state (³E manifold) was developed, mediated by Spin-Orbit (SO) coupling and Electron-Phonon interactions.
Quantum Application Relevance: The ISC mechanism is critical for the optical initialization and readout of the NV center’s electronic spin, enabling room-temperature applications in metrology and quantum information science.
Key Constraint Achieved: The model successfully constrained the previously unknown energy spacing ($\Delta$) between the spin-triplet (³E) and spin-singlet (¹A₁) levels to the range of 344 meV < $\Delta$ < 430 meV.
Material Requirement: The fidelity of this mechanism relies fundamentally on the intrinsic properties of the diamond lattice, necessitating high-purity, low-strain Single Crystal Diamond (SCD) for reliable defect engineering.
Engineering Pathway Identified: The research concludes that reducing the singlet-triplet spacing ($\Delta$) via strain application (e.g., uniaxial strain along the [111] axis) is a viable path to engineer the ISC rate, thereby improving spin initialization and readout fidelities.
6CCVD Value Proposition: 6CCVD provides the necessary Optical Grade SCD material and custom fabrication services (polishing, metalization, custom dimensions) required to replicate this research and implement strain-engineering solutions.

Technical Specifications

The following hard data points were extracted from the analysis of the NV center’s electronic structure and ISC rates:

Parameter	Value	Unit	Context
Ground State Splitting (D)	2.87	GHz	³A₂ manifold,
Visible Zero-Phonon Line (ZPL)	637	nm	³E $\rightarrow$ ³A₂ optical transition
Infrared ZPL Wavelength	1042	nm	¹A₁ $\rightarrow$ ¹E_1,2 optical transition
Radiative Decay Rate ($\Gamma_{Rad}$)	2$\pi$ $\times$ (13.2 $\pm$ 0.5)	MHz	³E manifold states
Measured ISC Rate ($\Gamma_{A1}/2\pi$)	16.0 $\pm$ 0.6	MHz	At cryogenic temperatures (Ref. 16)
Constrained Singlet-Triplet Spacing ($\Delta$)	344 to 430	meV	Energy spacing between ³E and ¹A₁
Acoustic Phonon Cutoff ($\Omega$)	74 to 93	meV	Extracted from ³A₂ $\rightarrow$ ³E absorption PSB
Low-Temperature Regime	5 to 26	K	Used for state-selective ISC rate measurements
High-Temperature Regime	295 to 700	K	Used for fluorescence lifetime comparison
Required $\Delta$ Reduction for Improvement	100 to 200	meV	Estimated reduction needed to achieve appreciable improvement in readout fidelity

Key Methodologies

The experimental and theoretical approach relied on precise control over material properties and advanced spectroscopic analysis:

Microscopic Model Formulation: Developed a second-order perturbation theory model treating the transverse Spin-Orbit (SO) interaction and E-symmetric Electron-Phonon interactions as time-dependent perturbations to the vibronic states of the ³E and ¹A₁ manifolds.
Vibrational Overlap Function (F($\omega$)) Extraction: The function F($\omega$), which describes the coupling between electronic and vibrational states, was approximated using the visible emission Phonon Sideband (PSB) spectrum of the ³E $\rightarrow$ ³A₂ transition measured at 4 K.
ISC Rate Calculation (Low-T): ISC rates were calculated using Fermi’s golden rule: first-order for $\Gamma_{A1}$ (SO coupling) and second-order for $\Gamma_{E1,2}$ (mediated by E-symmetric phonons coupling ³E states to ¹A₁).
Phonon Spectral Density: The E-symmetric acoustic phonon spectral density was modeled using the Debye model (proportional to $\omega^{3}$) and parameterized by the coupling strength ($\eta$).
Energy Spacing Constraint: Calculated ISC rates were compared against measured state-selective ISC rates at cryogenic temperatures (5 K) to constrain the unknown singlet-triplet energy spacing ($\Delta$) and the acoustic phonon cutoff ($\Omega$).
High-Temperature Modeling: The model was extended to high temperatures (up to 700 K) by incorporating temperature-dependent vibrational overlap functions and orbital averaging to predict fluorescence lifetimes.

6CCVD Solutions & Capabilities

This research highlights the critical role of high-quality diamond and precise engineering in advancing NV center quantum technology. 6CCVD is uniquely positioned to supply the necessary materials and customization required to replicate and extend this work, particularly in strain engineering for enhanced spin readout fidelity.

Research Requirement	6CCVD Solution & Capability	Technical Advantage
High-Purity, Low-Strain Diamond Host (Essential for stable NV centers and precise ISC control)	Optical Grade Single Crystal Diamond (SCD). Available in custom dimensions and thicknesses (0.1 µm to 500 µm).	Provides the ultra-low defect density and high crystalline quality necessary to minimize unwanted strain and maximize the quantum coherence of NV centers across the required temperature range (5 K to 700 K).
Strain Engineering for ISC Optimization (Requires custom geometry and surface quality to apply uniaxial strain and reduce $\Delta$)	Custom Dimensions and Polishing. Plates/wafers up to 125mm (PCD) or custom SCD sizes. Polishing to Ra < 1 nm (SCD) and Ra < 5 nm (PCD).	Enables the fabrication of micro/nanofabricated structures (e.g., membranes, cantilevers) where controlled, localized strain can be applied, directly addressing the paper’s conclusion regarding improving readout fidelity.
Integration of Control Electrodes (Needed for applying electric fields or local forces to induce strain)	Custom Metalization Services. In-house deposition of Au, Pt, Pd, Ti, W, Cu.	Allows researchers to integrate electrical contacts directly onto the diamond surface for active control of NV center properties (e.g., Stark shift, local strain application) and high-frequency measurements.
Robust Substrates for Thermal Testing (Required for stable mounting during 5 K to 700 K measurements)	Thick Substrates. SCD and PCD substrates available up to 10 mm thickness.	Ensures mechanical stability and efficient thermal management during extreme temperature cycling required for comprehensive characterization of the ISC mechanism.
Expert Consultation on Defect Physics (Guidance on material selection, orientation, and growth parameters)	In-house PhD Engineering Support. Dedicated team specializing in MPCVD growth parameters and quantum defect physics.	Accelerates research timelines by providing authoritative guidance on material specifications (e.g., specific N concentration, crystal orientation) for similar NV center quantum projects.

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

View Original Abstract

The intersystem crossing (ISC) is an important process in many solid-state atomlike impurities. For example, it allows the electronic spin state of the nitrogen-vacancy (NV) center in diamond to be initialized and read out using optical fields at ambient temperatures. This capability has enabled a wide array of applications in metrology and quantum information science. Here, we develop a microscopic model of the state-selective ISC from the optical excited state manifold of the NV center. By correlating the electron-phonon interactions that mediate the ISC with those that induce population dynamics within the NV center’s excited state manifold and those that produce the phonon sidebands of its optical transitions, we quantitatively demonstrate that our model is consistent with recent ISC measurements. Furthermore, our model constrains the unknown energy spacings between the center’s spin-singlet and spin-triplet levels. Finally, we discuss prospects to engineer the ISC in order to improve the spin initialization and readout fidelities of NV centers.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.91.165201