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Opportunities for Long-Range Magnon-Mediated Entanglement of Spin Qubits via On- and Off-Resonant Coupling

MetadataDetails
Publication Date2021-10-21
JournalPRX Quantum
AuthorsMasaya Fukami, Denis R. Candido, David D. Awschalom, Michael E. Flatté, Masaya Fukami
InstitutionsUniversity of Iowa, Argonne National Laboratory
Citations90
AnalysisFull AI Review Included

Technical Documentation & Analysis: Magnon-Mediated NV-NV Entanglement

Section titled “Technical Documentation & Analysis: Magnon-Mediated NV-NV Entanglement”

This research demonstrates the feasibility of achieving long-range entanglement between Nitrogen-Vacancy (NV) centers in diamond using Yttrium Iron Garnet (YIG) magnon modes, a critical step toward scalable solid-state quantum computing.

  • Long-Range Entanglement: Predicts strong, long-distance NV-NV coupling ($>$ ”m separation) mediated by magnon modes in ferromagnetic nanostructures (YIG waveguides and bars).
  • Ultra-High Performance: Achieves ultra-high cooperativity ($C \ge 10^{4}$) for on-resonant transduction and a Gate to Decoherence Ratio (GDR) of $\approx 10^{3}$ for off-resonant virtual-magnon exchange protocols.
  • High Fidelity & Robustness: The virtual-magnon exchange protocol yields high entanglement fidelity ($F \approx 0.95$ at T=70 mK) and is robust against thermal magnon fluctuations up to T $\le 150$ mK.
  • Material Requirements: Success hinges on integrating high-coherence NV centers in diamond extremely close to the YIG surface (NV height $h$ as low as 5 nm).
  • Optimal Geometry: Calculations provide optimal nanoscale YIG geometries (e.g., 5 nm thickness, 3 ”m length) necessary to discretize magnon modes and enhance coupling strength.
  • 6CCVD Value Proposition: 6CCVD specializes in the high-quality Single Crystal Diamond (SCD) required for this application, offering precise thickness control, ultra-smooth polishing, and custom dimensions essential for hybrid quantum device fabrication.

The following hard data points were extracted from the analysis of the hybrid NV-magnon system performance:

ParameterValueUnitContext
Maximum Operating Temperature$\le 150$mKRequired for useful entanglement
NV-NV Separation (High GDR)$> 2$”mAchieved GDR $\approx 10^{3}$
On-Resonance Cooperativity (C)$\ge 10^{4}$DimensionlessFinite length YIG bar
Off-Resonance GDR$\approx 10^{3}$DimensionlessFinite length YIG bar, 2 ”m separation
Entanglement Fidelity (Virtual Exchange)$\approx 0.95$DimensionlessT = 70 mK
Entanglement Fidelity (Transduction)$\approx 0.81$DimensionlessT = 70 mK
NV Center Coherence Time (T2)1msUsed in GDR calculation
YIG Bar Thickness (d)5nmOptimized nanoscale dimension
YIG Bar Length (l)3”mOptimized nanoscale dimension
NV Center Height (h)5 to 25nmDistance from YIG surface (critical parameter)
NV Zero-Field Splitting (DNV)$2\pi \times 2.877$GHzNV center property
Gilbert Damping Parameter ($\alpha$)$10^{-5}$DimensionlessOptimistic value used in simulation

The theoretical and numerical approach focused on modeling the quantum dynamics of the hybrid system under realistic conditions.

  1. Hybrid Device Modeling: NV centers in diamond were modeled as being placed directly on top of YIG ferromagnetic nanostructures (infinitely long waveguides or finite-length bars).
  2. Hamiltonian Formalism: The total system Hamiltonian ($H = H_{NV} + H_{m} + H_{int}$) was constructed using the dipole-exchange magnon formalism to accurately capture both magnetic dipole and quantum exchange interactions.
  3. Magnon Mode Diagonalization: The magnon Hamiltonian ($H_{m}$) was diagonalized using the Bogoliubov transformation, crucial for calculating the full magnonic properties of the finite-cross-section YIG structures.
  4. Effective NV-NV Coupling ($g_{eff}$): The effective coupling strength was calculated via the Schrieffer-Wolff transformation, showing rapid decay with detuning, enabling fast entangling gates.
  5. Protocol Comparison: Two entanglement protocols were analyzed using the Lindblad master equation at finite temperatures (T $\le 150$ mK):
    • On-resonant Transduction: Faster gate operation, but sensitive to magnon damping.
    • Off-resonant Virtual-Magnon Exchange: Slower, but more robust against thermal fluctuations and yields higher fidelity.
  6. Optimization Parameters: Performance metrics (Entanglement Rate, GDR) were analyzed as functions of critical geometric parameters, including YIG thickness ($d$) and NV center proximity ($h$).

The success of this quantum architecture relies fundamentally on the quality and precise integration of the diamond material. 6CCVD is uniquely positioned to supply the necessary MPCVD diamond components to replicate and advance this research.

To achieve the high coherence times ($T_{2} = 1$ ms) and low defect densities required for functional NV centers, Optical Grade Single Crystal Diamond (SCD) is mandatory.

6CCVD MaterialApplication Requirement6CCVD Capability Match
Optical Grade SCDHigh spin coherence, low background defects.SCD plates up to 500 ”m thick, optimized for NV creation (e.g., shallow implantation).
High-Purity SubstratesRobust platform for nanoscale YIG fabrication.Substrates available up to 10 mm thickness for mechanical stability.
Polishing QualityUltra-smooth surface required for nanoscale proximity ($h \le 25$ nm) to YIG.SCD polishing to Ra < 1 nm ensures minimal surface noise and optimal NV-YIG coupling.

The research highlights the critical role of nanoscale geometry (YIG dimensions, NV height $h$). 6CCVD provides the manufacturing flexibility necessary for hybrid device integration:

  • Custom Dimensions: We supply SCD wafers and plates in custom dimensions, facilitating integration with complex lithographic processes used to define YIG nanostructures. We offer PCD plates up to 125 mm in diameter.
  • Precise Thickness Control: We offer SCD material thicknesses ranging from 0.1 ”m to 500 ”m, allowing researchers to select the optimal diamond layer thickness for subsequent shallow NV implantation and YIG deposition.
  • Metalization Services: Although the paper focuses on YIG, future device integration requires electrical contacts. 6CCVD offers internal metalization capabilities, including Au, Pt, Pd, Ti, W, and Cu, enabling seamless integration of control lines and readout circuitry adjacent to the YIG structures.

6CCVD’s in-house team of PhD material scientists and engineers possesses deep expertise in MPCVD diamond growth and post-processing techniques essential for quantum applications.

We offer specialized consultation for projects involving NV-Magnon Hybrid Systems to assist with:

  • Optimizing diamond material selection for specific NV creation techniques (e.g., delta-doping or shallow implantation).
  • Defining precise polishing specifications (Ra) to minimize surface noise and maximize NV-YIG coupling strength.
  • Designing custom wafer geometries for compatibility with cryogenic (T $\le 150$ mK) experimental setups.

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

View Original Abstract

The ability to manipulate entanglement between multiple spatially separated qubits is essential for quantum-information processing. Although nitrogen-vacancy (NV) centers in diamond provide a promising qubit platform, developing scalable two-qubit gates remains a well-known challenge. To this end, magnon-mediated entanglement proposals have attracted attention due to their long-range spin-coherent propagation. Optimal device geometries and gate protocols of such schemes, however, have yet to be determined. Here we predict strong long-distance (>ÎŒm) NV-NV coupling via magnon modes with cooperativities exceeding unity in ferromagnetic bar and waveguide structures. Moreover, we explore and compare on-resonant transduction and off-resonant virtual-magnon exchange protocols, and discuss their suitability for generating or manipulating entangled states at low temperatures (T 150mK) under realistic experimental conditions. This work will guide future experiments that aim to entangle spin qubits in solids with magnon excitations.