Collective strong coupling with homogeneous Rabi frequencies using a 3D lumped element microwave resonator
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2016-07-18 |
| Journal | Applied Physics Letters |
| Authors | Andreas Angerer, Thomas Astner, Daniel Wirtitsch, Hitoshi Sumiya, Shinobu Onoda |
| Institutions | University of Tsukuba, Sumitomo Electric Industries (Japan) |
| Citations | 35 |
| Analysis | Full AI Review Included |
Technical Analysis of Collective Strong Coupling in Diamond NV Centers
Section titled âTechnical Analysis of Collective Strong Coupling in Diamond NV CentersâThis documentation analyzes the key findings, methodologies, and material requirements presented in the research paper âCollective Strong Coupling with Homogeneous Rabi Frequencies using a 3D Lumped Element Microwave Resonator.â This analysis is tailored to demonstrate how 6CCVDâs specialized MPCVD diamond capabilities can facilitate the replication and advancement of this critical quantum research.
Executive Summary
Section titled âExecutive SummaryâThe research successfully achieved the strong coupling regime of Cavity Quantum Electrodynamics (QED) using a macroscopic ensemble of Nitrogen-Vacancy (NV) centers in diamond coupled to a custom 3D lumped element resonator (LER).
- Homogeneity Achievement: The novel LER design focuses the magnetic field, achieving outstanding homogeneity (RMS deviation of $1.54%$) across the diamond sample volume, a critical step for coherent manipulation of the entire spin ensemble.
- Strong Coupling: A high collective coupling strength ($\Omega = 12.46$ MHz) was observed, significantly exceeding the cavity linewidth ($\kappa$) and spin inhomogeneous linewidth ($\gamma^*$), resulting in a cooperativity factor ($C$) of approximately 27.
- Enhanced Single Spin Rate: The optimized small mode volume yielded a high single spin coupling rate of $|g_{0}| \approx 70$ mHz, more than an order of magnitude higher than standard 3D cavities.
- Material Basis: The experiment relied on a synthetic type-Ib HPHT diamond host, post-processed via 2 MeV electron irradiation and subsequent high-temperature annealing to achieve a high NV concentration ($\approx 40$ ppm).
- Engineering Focus: The implementation required stringent material processing, including polishing metallic resonator surfaces ($R_{a} < 0.25$ ”m) and precise dimensional control of the diamond substrate ($4.2 \times 3.4 \times 0.92$ mm).
- Quantum Implications: This work establishes a platform for interfacing macroscopic spin ensembles with microwave circuits, paving the way for scalable, coherent quantum information protocols based on solid-state defects.
Technical Specifications
Section titled âTechnical SpecificationsâThe following table extracts the critical hard data points defining the performance and materials used in the experiment.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Collective Coupling Strength ($\Omega$) | 12.46 | MHz | Observed avoided crossing, confirming strong coupling. |
| Cooperativity Factor ($C$) | $\approx 27$ | (Unitless) | Calculated as $\Omega^{2}/(\kappa \gamma^{*})$. |
| Single Spin Coupling Rate ($ | g_{0} | $) | $\approx 70$ |
| Field Homogeneity (RMS Deviation) | 1.54 | % | RMS deviation of magnetic field component over sample volume. |
| Loaded Cavity Resonance Frequency ($\nu$) | 3.121 | GHz | Measured with the NV diamond sample loaded. |
| Loaded Quality Factor ($Q$) | 1637 | (Unitless) | Measured with far detuned spins. |
| Cavity Linewidth ($\kappa$) (HWHM) | 1.91 | MHz | Derived from loaded $Q$. |
| Spin Ensemble Linewidth ($\gamma^{*}$) (HWHM) | $\approx 3$ | MHz | Inhomogeneously broadened linewidth estimate. |
| Diamond Sample Dimensions | $4.2 \times 3.4 \times 0.92$ | mm | Substrate dimensions, leading to $N \approx 10^{17}$ spins. |
| NV Concentration (Approximate) | 40 | ppm | Final concentration after irradiation/annealing. |
| Operating Temperature | 25 | mK | Provided by dilution refrigerator for thermal polarization. |
| Required Resonator Surface Roughness | $< 0.25$ | ”m | For minimizing ohmic losses in metallic structures. |
Key Methodologies
Section titled âKey MethodologiesâThe core scientific achievement hinged on combining novel resonator architecture with precise solid-state material engineering.
- Resonator Design: Developed a 3D Lumped Element Resonator (LER) utilizing counter-propagating currents in âbow-tieâ metallic structures to focus and amplify the AC magnetic field into a small mode volume, ensuring homogeneous field distribution.
- Resonator Fabrication: The cavity was machined from Oxygen Free Copper ($99.997%$ purity) to allow for external magnetic field penetration necessary for Zeeman tuning.
- Loss Reduction: Mechanical surface treatment and polishing were performed on all metallic surfaces to achieve a roughness $R_{a} < 0.25$ ”m, minimizing ohmic losses proportional to surface roughness and skin depth.
- Diamond Host Preparation: A synthetic type-Ib High Pressure High Temperature (HPHT) diamond with an initial nitrogen concentration of 100 ppm was selected.
- NV Center Creation: NV centers were generated by irradiating the diamond with 2 MeV electrons at 800 °C, reaching a total dose of $1.1 \times 10^{19}$ cm-2, followed by multiple high-temperature annealing steps at 1000 °C to stabilize the vacancy population, resulting in $\approx 40$ ppm NV centers.
- QED Setup: The diamond sample was mounted in the LER, placed in a dilution refrigerator operating at 25 mK, and coupled to the external environment via coaxial ports.
- Zeeman Tuning: A 3D Helmholtz coil configuration provided the necessary homogeneous external d.c. magnetic field to tune the NV electronic spin transitions into resonance with the cavity mode (3.121 GHz).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research highlights the need for ultra-precise diamond material specifications to achieve advanced solid-state quantum systems. 6CCVD is uniquely positioned to supply the next generation of materials required to replicate, scale, and optimize this type of Cavity QED experiment.
| Requirement from Paper | 6CCVD Solution & Capability | Benefit to Customer |
|---|---|---|
| High-Purity Host Material for NV Creation | Electronic Grade Single Crystal Diamond (SCD). Our MPCVD process offers superior control over impurity incorporation compared to legacy HPHT. | Enables highly controlled NV center generation (PPM to PPB level) via irradiation/implantation, crucial for managing the spin ensemble linewidth ($\gamma^{*}$). |
| Precise Dimensions and Thickness (Sample size: $4.2 \times 3.4 \times 0.92$ mm) | Custom Substrates up to 10 mm: 6CCVD specializes in cutting, grinding, and polishing custom plates and wafers up to $125$ mm (PCD). | Perfect dimensional matching ensures seamless integration into the small mode volume 3D LER, optimizing coupling efficiency and minimizing field non-uniformity. |
| Surface Quality for QED Performance | Ultra-Smooth SCD Polishing: We offer $R_{a} < 1$ nm polishing (SCD), significantly exceeding standard commercial quality. | A low-defect, ultra-smooth diamond surface minimizes surface loss mechanisms and defect-induced decoherence, critical for 25 mK cryogenic operation. |
| Potential Superconducting Cavity Integration | Advanced Metalization Services (Au, Pt, Ti, Cu): 6CCVD provides in-house metal deposition (e.g., Ti/Pt/Au stacks). | Supports the shift toward high-Q superconducting cavities (mentioned on page 7), facilitating low-loss contacts or bonding for hybrid quantum circuits. |
| Extension to BDD Technology (Not in paper, but a natural quantum extension) | Boron-Doped Diamond (BDD) Films: Custom BDD growth capability for realizing novel cavity QED systems utilizing spin qubits in doped silicon or shallow donor systems. | Allows researchers to pivot to alternative solid-state spin qubits, leveraging diamondâs wide bandgap properties. |
Engineering Support
Section titled âEngineering Supportâ6CCVD recognizes that successful implementation of complex QED protocols is highly dependent on the quality and specificity of the diamond host material. Our in-house PhD team provides specialized engineering support for projects requiring custom nitrogen incorporation, specific crystal orientation, and post-processing consultation (e.g., optimizing irradiation and annealing parameters for high-fidelity NV center creation).
Call to Action:
For custom specifications or material consultation on high-purity Single Crystal Diamond (SCD) substrates for quantum computation or advanced microwave electronics, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).
View Original Abstract
We design and implement 3D-lumped element microwave cavities that spatially focus magnetic fields to a small mode volume. They allow coherent and uniform coupling to electron spins hosted by nitrogen vacancy centers in diamond. We achieve large homogeneous single spin coupling rates, with an enhancement of more than one order of magnitude compared to standard 3D cavities with a fundamental resonance at 3 GHz. Finite element simulations confirm that the magnetic field distribution is homogeneous throughout the entire sample volume, with a root mean square deviation of 1.54%. With a sample containing 1017 nitrogen vacancy electron spins, we achieve a collective coupling strength of Ω = 12 MHz, a cooperativity factor C = 27, and clearly enter the strong coupling regime. This allows to interface a macroscopic spin ensemble with microwave circuits, and the homogeneous Rabi frequency paves the way to manipulate the full ensemble population in a coherent way.