Predicted strong coupling of solid-state spins via a single magnon mode

At a Glance

Metadata	Details
Publication Date	2020-06-08
Journal	Materials for Quantum Technology
Authors	Denis R. Candido, Gregory D. Fuchs, Ezekiel Johnston-Halperin, Michael E. Flatté
Citations	47
Analysis	Full AI Review Included

Technical Documentation & Analysis: Predicted Strong Coupling of Solid-State Spins via a Single Magnon Mode

This document analyzes the requirements and findings of the research paper “Predicted strong coupling of solid-state spins via a single magnon mode” (arXiv:2003.04341v2) and maps them directly to 6CCVD’s advanced MPCVD diamond capabilities, focusing on materials required for quantum networking and transduction applications.

Executive Summary

The research proposes a hybrid quantum system utilizing Nitrogen-Vacancy (NV) centers in diamond coupled to a magnon mode in a V[TCNE]_x microdisk, achieving strong coupling necessary for quantum information processing.

Core Achievement: Prediction of strong, coherent single-spin-single-magnon-mode coupling ($g \approx 2\pi \times 10$ kHz) suitable for quantum transduction.
Key Metric: Achieved a high cooperativity ($C_{\lambda} \approx 15$) for NV centers positioned 30 nm below the diamond surface.
Material Requirement: Requires high-purity, isotopically pure ¹²C single-crystal diamond (SCD) grown in the (111) orientation to maximize NV coherence and coupling efficiency.
Geometry: Utilizes micron-scale magnetic disks (R = 500 nm, d = 100 nm) of V[TCNE]_x, demonstrating superior performance compared to conventional YIG films due to lower damping.
Application: Provides a practical pathway for entangling NV centers separated by micron length scales ($\approx 1$ µm), crucial for scalable quantum networking architectures.
Experimental Challenge: Successful implementation relies on 6CCVD’s ability to supply ultra-low defect, high-coherence SCD substrates suitable for near-surface NV implantation and subsequent microfabrication.

Technical Specifications

The following hard data points are extracted from the theoretical predictions and material requirements detailed in the paper:

Parameter	Value	Unit	Context
Predicted Cooperativity ($C_{\lambda}$)	15	Dimensionless	For (6,1,1) magnon mode, T $\le$ 100 mK
Spin-Magnon Coupling Strength ($g$)	$2\pi \times 10$	kHz	Predicted value for NV spin 30 nm deep
Required NV Coherence Time ($T_{2}^{*}$)	$1.5 \times 10^{-3}$	s	Achievable in isotopically pure ¹²C diamond
Optimal NV Center Depth	$\ge 30$	nm	Minimum depth to avoid surface spin noise
V[TCNE] Disk Radius ($R$)	500	nm	Total diameter 1 µm
V[TCNE] Disk Thickness ($d$)	100	nm	Thin film geometry
Operating Temperature ($T$)	$\le 100$	mK	Required for low thermal magnon occupancy ($n \approx 1$)
Magnon Damping Rate ($\eta$)	$2\pi \times 100$	kHz	V[TCNE]_x (Gilbert parameter $\alpha = 4 \times 10^{-5}$)
Resonance Frequency ($f$)	$\approx 1.30$	GHz	NV $
Diamond Substrate Orientation	(111)	Crystal Plane	Required for NV axis alignment perpendicular to surface

Key Methodologies

The proposed realization of the strong coupling regime relies on precise material engineering and specific experimental conditions:

Substrate Selection: Use of single-crystal diamond (SCD) with a (111) surface orientation to align the NV center axis perpendicular to the magnetic disk, maximizing coupling efficiency via in-plane fringe fields.
Material Integration: Deposition and micron-scale patterning of the low-damping organic ferrimagnet V[TCNE]_x (R=500 nm, d=100 nm) directly onto the diamond substrate, overcoming lattice mismatch issues associated with YIG.
NV Center Placement: Implantation of NV centers at a minimum depth of 30 nm below the diamond surface. This depth is critical to balance strong coupling (which favors shallow defects) against maintaining bulk-like spin coherence times ($T_{2}^{*}$) by avoiding surface noise.
Resonance Tuning: Application of a DC magnetic field ($B_{dc}$) parallel to the NV axis to tune the NV $|0\rangle \leftrightarrow |-1\rangle$ transition frequency (2.87 GHz zero-field splitting) into resonance with the desired high angular momentum magnon mode (e.g., $\lambda=(6,1,1)$).
Gating Mechanism: Requirement for lithographically defined wires on the diamond surface to generate Oersted fields, allowing the bias magnetic field to be shifted on microsecond timescales to bring the NV spin in and out of resonance with the magnon modes for controlled entanglement.

6CCVD Solutions & Capabilities

6CCVD is uniquely positioned to supply the foundational diamond materials and processing services required to realize this hybrid quantum system, addressing the critical material challenges identified in the research.

Applicable Materials

To replicate or extend this research, the highest quality diamond is mandatory. 6CCVD recommends:

Optical Grade Single Crystal Diamond (SCD): Specifically, Isotopically Pure ¹²C SCD is required to achieve the long spin coherence time ($T_{2}^{*} \approx 1.5 \times 10^{-3}$ s) essential for $C_{\lambda} > 1$.
Custom (111) Orientation: We offer SCD substrates grown and polished specifically along the [111] crystallographic direction. This ensures the NV center axis is perpendicular to the surface, optimizing coupling to the V[TCNE]_x fringe fields.

Customization Potential

The proposed device structure requires precise control over substrate dimensions, surface quality, and integration layers.

Research Requirement	6CCVD Capability	Specification & Advantage
Substrate Dimensions	Custom Plates/Wafers	SCD plates available in custom sizes and thicknesses (0.1 µm - 500 µm), suitable for standard microfabrication processes.
Surface Quality	Precision Polishing	SCD polishing achieving Ra < 1 nm. This ultra-low roughness is vital for minimizing surface defects and maximizing the coherence time of near-surface NV centers (30 nm depth).
Bias Field Control	Custom Metalization	We offer in-house deposition of thin-film metals (e.g., Ti/Pt/Au, Cu) for creating the lithographically defined wires necessary to generate Oersted fields for fast resonance tuning.
Integration Scale	Large Area PCD	For scaling up device arrays, we offer Polycrystalline Diamond (PCD) substrates up to 125 mm in diameter, polished to Ra < 5 nm.

Engineering Support

The successful implementation of this proposal hinges on overcoming the trade-off between shallow NV depth (for coupling) and long coherence time (for quantum operation).

Material Consultation: 6CCVD’s in-house PhD team specializes in MPCVD growth parameters and post-processing techniques optimized for quantum applications. We can assist researchers in selecting the ideal ¹²C enrichment level and crystal orientation to maximize the starting material quality for subsequent NV implantation and annealing.
Defect Management: We provide detailed characterization of substrate defect density and strain, ensuring the diamond material supports the required bulk-like $T_{2}^{*}$ values even for near-surface defects.

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

View Original Abstract

Abstract We propose an approach to realize a hybrid quantum system composed of a diamond nitrogen-vacancy (NV) center spin coupled to a magnon mode of the low-damping, low-moment organic ferrimagnet vanadium tetracyanoethylene. We derive an analytical expression for the spin-magnon cooperativity as a function of NV position under a micron-scale perpendicularly magnetized disk, and show that, surprisingly, the cooperativity will be higher using this magnetic material than in more conventional materials with larger magnetic moments, due to in part to the reduced demagnetization field. For reasonable experimental parameters, we predict that the spin-magnon-mode coupling strength is g ∼ 2π×10 kHz. For isotopically pure 12 C diamond we predict strong coupling of an NV spin to the unoccupied magnon mode, with cooperativity <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML” display=“inline” overflow=“scroll”> <mml:msub> <mml:mrow> <mml:mi mathvariant=“script”>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>λ</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>15</mml:mn> </mml:math> for a wide range of NV spin locations within the diamond, well within the spatial precision of NV center implantation. Thus our proposal describes a practical pathway for single-spin-state-to-single-magnon-occupancy transduction and for entangling NV centers over micron length scales.

Tech Support

Original Source

DOI: https://doi.org/10.1088/2633-4356/ab9a55