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Towards achieving strong coupling in three-dimensional-cavity with solid state spin resonance

MetadataDetails
Publication Date2016-04-15
JournalJournal of Applied Physics
AuthorsJean-Michel Le Floch, Nicolas Delhote, Michel Aubourg, Valérie Madrangeas, D. Cros
InstitutionsUniversité de Limoges, Centre National de la Recherche Scientifique
Citations20
AnalysisFull AI Review Included

6CCVD Technical Documentation: Strong Coupling in 3D-Cavities using NV-Diamond

Section titled “6CCVD Technical Documentation: Strong Coupling in 3D-Cavities using NV-Diamond”

This document analyzes the technical requirements and achievements detailed in the paper, “Towards achieving strong coupling in 3D-cavity with solid state spin resonance,” and aligns them with 6CCVD’s advanced Monocrystalline and Polycrystalline Chemical Vapor Deposition (MPCVD) diamond capabilities.


This research establishes new benchmarks for achieving strong and ultra-strong collective coupling between microwave resonant photons and ensembles of Nitrogen Vacancy (NV) centers in diamond using optimized 3D cavity designs.

  • Core Achievement: Successful numerical modeling and design of novel 3D cavities to maximize collective spin coupling (gc) and cooperative factor (C).
  • Performance Metrics: Demonstrated a calculated maximum cooperative factor (C) of 2,027 using a high-Q TE* double-split resonator design, significantly surpassing previous 1D coplanar waveguide (CPW) approaches.
  • Magnetic Confinement: Introduced an Unloaded Hybrid Cavity topology achieving a magnetic filling factor (pm) of 0.47, representing a four-fold increase in magnetic field confinement into the diamond sample compared to prior state-of-the-art superconducting CPW cavities.
  • Material Requirements: Confirms the critical need for ultra-high-purity, low-loss single crystal diamond (SCD) samples with high, controlled NV spin densities, operated at cryogenic temperatures (4K).
  • Design Target: Optimized cavity resonance frequency to match the NV ground state transition at 2.87 GHz.
  • Future Implications: These robust 3D designs open the door to ultra-strong coupling regimes, requiring fewer NV spins and offering greater design flexibility for quantum computing architectures and fundamental physics tests.

The following key technical parameters were extracted from the simulation and design results, focusing on the highest performing cavity topologies (TE* Double-Split Resonator and Unloaded Hybrid Cavity).

ParameterValueUnitContext
Target Resonance Frequency2.87 ± 0.02GHzMatches NV ground state ms=0 to ms=±1 transition
Operating Temperature4KCryogenic simulation temperature
Max Cooperative Factor (C)2,027-Achieved by TE* Double-Split Resonator design
Max Magnetic Filling Factor (pm)0.471-Achieved by Unloaded Hybrid Cavity (4x improvement vs. CPW)
Max Unloaded Q-Factor (Q0)300,000-Achieved by TE* Double-Split Resonator (optimized dielectric loading)
Collective Coupling Strength (gc)102MHzAchieved by Unloaded Hybrid Cavity
Spin Ensemble Density ($\rho$)1.2 x 106”m-3Assumed density for HPHT diamond simulation
Diamond Sample Size3 x 3 x 1.5mmDielectric sample size used in the cavities
Spin Linewidth ($\gamma$s/2$\pi$)≈ 3MHzAssumed linewidth at 4K
Cavity MetalCopper (Rs=5.77 mΩ)-Material used for standard cavity walls at 4K

The study relied on rigorous numerical analysis and advanced materials engineering to optimize coupling parameters in 3D space.

  1. Numerical Simulation: Conducted 3D Finite-Element Analysis (FEA) using specialized software to model microwave magnetic field confinement within various cavity geometries.
  2. Geometry Optimization: Investigated multiple cavity topologies, including waveguide-based, high-Q dielectric resonators (Bragg, WGM), reentrant cavities, and the novel Double-Split and Hybrid designs, focusing on minimizing mode volume and maximizing AC-magnetic field density (pm).
  3. Material Selection: Focused exclusively on low-loss dielectrics (diamond, TiO2 rutile, Al2O3 sapphire) and highly conductive metals (Copper, Niobium post) to minimize damping rates ($\kappa$ and $\gamma$s) and maximize Q-factor at 4K.
  4. NV Alignment: Assumed optimal mechanical alignment of the diamond sample inside the cavity to ensure two sub-ensembles of NV defects were correctly oriented (45°) relative to the applied DC magnetic field (BDC), maximizing the number of coupled spins.
  5. Coupling Calculation: Determined the performance via the Cooperative Factor (C = gc2 / (2$\kappa$c$\gamma$s)) and collective coupling strength (gc), validating results against established 1D CPW resonator measurements.

6CCVD is uniquely positioned to supply the advanced diamond materials and precision engineering services required to replicate and extend this strong coupling research into commercial quantum applications. The key to this success is delivering diamond substrates with precise geometric dimensions, ultra-low dielectric loss properties, and controlled spin defect concentration.

Research Requirement6CCVD Applicable Materials & ServicesTechnical Value Proposition
Required Material: Ultra-high purity single crystal diamond (SCD) for NV ensemble coherence (low $\tan \delta$).Optical Grade SCD: SCD wafers and substrates grown via MPCVD, providing ultra-low strain and defect density precursors necessary for subsequent NV creation (via irradiation/annealing). Available in thicknesses from 0.1”m up to 500”m.Minimizes intrinsic dielectric losses ($\tan \delta$) and cavity damping rates, essential for maximizing the Q-factor (Q0 up to 300,000 required) in cryogenic quantum architectures.
Custom Dimensions: Precision diamond inserts (e.g., 3 x 3 x 1.5 mm) for field confinement.Custom Substrate Dicing & Laser Cutting: We provide full customization of plate dimensions up to 125mm (PCD) and precise dicing of SCD substrates to fit highly constrained 3D cavity architectures.Ensures tight mechanical fitting and optimal positioning within the cavity magnetic field maxima, crucial for achieving the maximum magnetic filling factor (pm=0.47) demonstrated by the hybrid cavity.
Surface Quality: Ultra-smooth surfaces to minimize extrinsic microwave loss mechanisms.Sub-Nanometer Polishing: Guaranteed polishing finish of Ra < 1nm for SCD and Ra < 5nm for inch-size PCD.Reduces surface scattering and parasitic losses, protecting the coherence time of the coupled spin ensemble in the ultra-strong coupling regime.
Metalization Integration: Requirement for highly conductive or superconducting elements (e.g., Niobium post) within the hybrid cavity design.Internal Metalization Services (Au, Pt, Pd, Ti, W, Cu): 6CCVD can integrate custom metal contact pads or boundary layers directly onto the diamond substrate using Ti/Pt/Au or other specified materials to facilitate device integration and hybridization.Reduces material interfaces and fabrication steps, ensuring the integrity of low-loss metallic contacts required for cryogenic operation.
NV Optimization: Need for diamond material with optimized, preferentially aligned NV spins (e.g., via [111] growth).Engineering Support: Our in-house PhD team provides expert consultation on material specification, including optimizing nitrogen incorporation and crystallographic orientation for post-growth NV formation, maximizing the percentage of actively coupled spins.Accelerates R&D cycles by ensuring the material inputs are optimally matched to the quantum application’s requirements.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We support global shipping (DDU default, DDP available).

View Original Abstract

We investigate the microwave magnetic field confinement in several microwave three-dimensional (3D)-cavities, using a 3D finite-element analysis to determine the best design and achieve a strong coupling between microwave resonant cavity photons and solid state spins. Specifically, we design cavities for achieving strong coupling of electromagnetic modes with an ensemble of nitrogen vacancy (NV) defects in diamond. We report here a novel and practical cavity design with a magnetic filling factor of up to 4 times (2 times higher collective coupling) than previously achieved using one-dimensional superconducting cavities with a small mode volume. In addition, we show that by using a double-split resonator cavity, it is possible to achieve up to 200 times better cooperative factor than the currently demonstrated with NV in diamond. These designs open up further opportunities for studying strong and ultra-strong coupling effects on spins in solids using alternative systems with a wider range of design parameters. The strong coupling of paramagnetic spin defects with a photonic cavity is used in quantum computer architecture, to interface electrons spins with photons, facilitating their read-out and processing of quantum information. To achieve this, the combination of collective coupling of spins and cavity mode is more feasible and offers a promising method. This is a relevant milestone to develop advanced quantum technology and to test fundamental physics principles.