State-dependent phonon-limited spin relaxation of nitrogen-vacancy centers
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-02-09 |
| Journal | Physical Review Research |
| Authors | Matthew Carl Cambria, Aedan Gardill, Y. Li, Ariel Norambuena, J. R. Maze |
| Institutions | University of WisconsinâMadison, Universidad Mayor |
| Citations | 16 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Phonon-Limited Spin Relaxation in NV Centers
Section titled âTechnical Documentation & Analysis: Phonon-Limited Spin Relaxation in NV CentersâReference Paper: Cambria et al., State-dependent phonon-limited spin relaxation of nitrogen-vacancy centers (arXiv:2007.11529v1, 2020).
Executive Summary
Section titled âExecutive SummaryâThis research establishes the fundamental phonon-limited constraints on the electronic spin coherence time ($T_{2, \text{max}}$) of nitrogen-vacancy (NV) centers in high-purity bulk diamond at room temperature (295 K).
- Coherence Limit Defined: The maximum theoretically achievable coherence time ($T_{2, \text{max}}$) for the NV electronic spin is limited to 6.8(2) ms in the single-quantum basis ($|m_{s} = 0\rangle \leftrightarrow |m_{s} = \pm 1\rangle$).
- State-Dependent Relaxation: The spin-lattice relaxation rate ($\gamma$) for the qutrit transition ($|m_{s} = -1\rangle \leftrightarrow |m_{s} = +1\rangle$) is approximately twice the rate ($\Omega$) for the qubit transition ($|m_{s} = 0\rangle \leftrightarrow |m_{s} = \pm 1\rangle$).
- Phonon-Limited Purity: Relaxation rates ($\gamma$ and $\Omega$) were found to be independent of native NV concentration across four orders of magnitude (10-5 to 10-1 ppb), confirming that spin-phonon interactions, not defect concentration, are the dominant limiting mechanism in high-purity CVD diamond.
- Mechanism Identification: The results suggest that Orbach-like processes involving two quasilocalized phonons, or contributions from higher-order terms in the spin-phonon Hamiltonian, are the dominant source of relaxation on the critical qutrit transition.
- Implication for Sensing: The study underscores the necessity of treating the NV as a three-level qutrit system, as population leakage to the third state occurs faster than relaxation within the simplified qubit subspace.
Technical Specifications
Section titled âTechnical SpecificationsâExtracted hard data points and measured parameters from the experimental results:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Maximum Coherence Time (T2,max) | 6.8(2) | ms | Single-quantum basis, 295 K |
| T2,max (Double-Quantum Basis) | 5.7(2) | ms | Double-quantum basis, 295 K |
| Qutrit Relaxation Rate ($\gamma$) | 117(5) | s-1 | Weighted average, small off-axis B field |
| Qubit Relaxation Rate ($\Omega$) | 59(2) | s-1 | Weighted average, small off-axis B field |
| Relaxation Rate Ratio ($\gamma / \Omega$) | ~2 | Dimensionless | Consistent across all measured samples |
| Operating Temperature | 295 ± 1 | K | Ambient conditions (Room Temperature) |
| NV Concentration Range Tested | 10-5 to 10-1 | ppb | Native NVs in bulk CVD diamond |
| Estimated Substitutional Nitrogen (Sample A) | 3 x 10-3 | ppb | Lowest concentration sample (Element Six) |
| Quasilocalized Phonon Energy ($\hbar\omega_{loc}$) | 65 | meV | Consistent with ab initio calculations |
| Idealized Minimum Magnetic Sensitivity ($\delta B_{min}$) | 69(1) | pT/âHz | Calculated using T2,max (C=1) |
Key Methodologies
Section titled âKey MethodologiesâThe experimental approach relied on high-quality MPCVD diamond and precise optical/magnetic control to isolate phonon-limited dynamics.
- Material Sourcing: Experiments utilized native NV centers in three distinct high-purity, bulk, CVD-grown diamond samples from different commercial suppliers (Element Six, Diamond Elements, Chenguang).
- Purity Range: Samples were selected to cover a wide range of native NV concentrations, confirming the independence of relaxation rates from defect density.
- Measurement Platform: A homebuilt confocal microscope was used, maintained at a temperature stable to 295 K (±1 K).
- Spin Control: Spin polarization and readout were achieved using approximately 1 mW of 532-nm light.
- Rate Extraction Technique: State-selective $\pi$-pulses were applied, and a classical three-level population model was used to measure population decay curves. Subtraction of these curves yielded single-exponential decays, allowing isolation of the qubit ($\Omega$) and qutrit ($\gamma$) relaxation rates.
- Magnetic Environment: Measurements were primarily conducted under small off-axis magnetic fields (Bâ„ < 1 G) to ensure superior phonon-limited coherence times, minimizing external noise sources.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research confirms that achieving maximum NV coherence requires ultra-high-purity diamond where relaxation is dominated by intrinsic spin-phonon interactions, not extrinsic defects. 6CCVD is uniquely positioned to supply the materials and customization necessary to replicate and advance this critical quantum research.
Applicable Materials for Quantum Coherence
Section titled âApplicable Materials for Quantum CoherenceâTo replicate the phonon-limited regime demonstrated in this paper, researchers require diamond with extremely low nitrogen content and high crystalline quality.
| Research Requirement | 6CCVD Material Solution | Technical Specification |
|---|---|---|
| Ultra-High Purity Substrates | Optical Grade Single Crystal Diamond (SCD) | Nitrogen concentration typically < 1 ppb. Ensures relaxation is phonon-limited, maximizing T2. |
| Controlled Doping/Defect Creation | Custom Doped SCD | Precise control over nitrogen incorporation during MPCVD growth to achieve specific, low NV concentrations (e.g., the 10-5 ppb regime of Sample A). |
| High-Volume Sensing Ensembles | Polycrystalline Diamond (PCD) | Wafers up to 125 mm diameter for large-scale ensemble sensing applications requiring high material uniformity. |
| Charge State Control | Boron-Doped Diamond (BDD) | Available for engineering the Fermi level to stabilize the NV- charge state, critical for quantum applications. |
Customization Potential
Section titled âCustomization PotentialâThe study utilized bulk CVD diamond. 6CCVD offers extensive customization capabilities essential for both bulk and next-generation shallow NV experiments.
- Custom Dimensions: We provide SCD substrates up to 10 mm thick and PCD plates up to 125 mm in diameter, allowing for replication of bulk studies or development of large-area sensors.
- Advanced Polishing: While this paper focused on bulk NVs, future work on near-surface NVs (where surface noise is dominant) requires pristine surfaces. 6CCVD offers:
- SCD Polishing: Surface roughness Ra < 1 nm.
- PCD Polishing: Surface roughness Ra < 5 nm (for inch-size wafers).
- Integrated Device Fabrication: The theoretical discussion references the need for magnetic field control and potential electric field noise mitigation. 6CCVD provides in-house metalization services (Au, Pt, Pd, Ti, W, Cu) for direct integration of microwave antennas, electrodes, or contact pads onto the diamond surface.
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house PhD team specializes in material science for quantum applications. We offer consultation services to assist researchers in selecting the optimal material specifications (purity, orientation, thickness, and doping) required to replicate or extend this research on Phonon-Limited NV Spin Dynamics and Quantum Sensing projects.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Understanding the limits to the spin coherence of the nitrogen-vacancy (NV) center in diamond is vital to realizing the full potential of this quantum system. We show that relaxation on the |m<sub>s</sub> = -1> â|m<sub>s</sub> = +1> transition occurs approximately twice as fast as relaxation on the |m<sub>s</sub> = 0> â|m<sub>s</sub> = ±1> transitions under ambient conditions in native NVs in high-purity bulk diamond. The rates we observe are independent of NV concentration over four orders of magnitude, indicating they are limited by spin-phonon interactions. We find that the maximum theoretically achievable coherence time for an NV at 295 K is limited to 6.8(2) ms. Lastly, we present a theoretical analysis of our results that suggests Orbach-like relaxation from quasilocalized phonons or contributions due to higher-order terms in the spin-phonon Hamiltonian are the dominant mechanism behind |m<sub>s</sub> = -1> â|m<sub>s</sub> = +1> relaxation, motivating future measurements of the temperature dependence of this relaxation rate.