Fast Relaxation on Qutrit Transitions of Nitrogen-Vacancy Centers in Nanodiamonds
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-03-04 |
| Journal | Physical Review Applied |
| Authors | Aedan Gardill, Matthew Carl Cambria, Shimon Kolkowitz |
| Institutions | University of WisconsinâMadison |
| Citations | 15 |
| Analysis | Full AI Review Included |
Technical Documentation and Analysis: Fast Relaxation in NV Nanodiamonds
Section titled âTechnical Documentation and Analysis: Fast Relaxation in NV NanodiamondsâReference: Gardill, A., Cambria, M. C., & Kolkowitz, S. (2020). Fast relaxation on qutrit transitions of nitrogen-vacancy centers in nanodiamonds. arXiv:1910.10813v4.
Executive Summary
Section titled âExecutive SummaryâThis research identifies surface electric field noise as the dominant mechanism limiting the coherence time ($T_2$) of Nitrogen-Vacancy (NV) centers in commercial nanodiamonds (NDs), critically impacting their utility as quantum sensors.
- Decoherence Mechanism: Spin relaxation on the qutrit transition ($|H;\pm 1\rangle$) is found to be extremely fast ($\gamma$ up to 240 kHz), exceeding the desired qubit transition rate ($\Omega$) by orders of magnitude.
- Limitation: This fast relaxation limits the maximum achievable coherence time ($T_{2,max}$) in nanodiamonds to tens of microseconds (as low as 8.3 ”s), roughly two orders of magnitude shorter than expected if the NV spin were treated solely as a qubit.
- Root Cause: The high relaxation rate is directly correlated with frequency splitting ($\Delta_{\pm}$), showing a strong $1/f^2$ falloff indicative of resonant surface electric field noise (charge noise) emanating from fluctuating dipoles or charge traps.
- Mitigation Strategy: Researchers recommend that coherent measurements in NDs should be performed at moderate axial magnetic fields (> 60 G) to increase the level splitting ($\Delta_{\pm}$) and minimize the disruptive electric field noise.
- 6CCVD Solution: The use of commercial HPHT-derived nanodiamonds (with high intrinsic nitrogen levels and uncontrolled surfaces) is identified as the source of noise. 6CCVD specializes in high-purity, low-strain MPCVD Single Crystal Diamond (SCD) and Polycrystalline Diamond (PCD) wafers, which allow for controlled creation of NVs with ultra-low nitrogen concentrations and superior surface control, essential for unlocking long $T_2$ performance.
Technical Specifications
Section titled âTechnical SpecificationsâExtracted quantitative parameters relating to material characteristics, performance limitations, and measurement conditions:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Nanodiamond Source | AdĂĄmas Nano | N/A | Crushed HPHT monocrystalline microdiamonds |
| Nanodiamond Mean Diameter | 40 | nm | Full width at half maximum (FWHM) also ~40 nm |
| Pre-Irradiation N Concentration | ~100 | ppm | Substitutional nitrogen in starting material |
| Post-Processing N Concentration | ~60 - 80 | ppm | After irradiation and annealing |
| Annealing Temperature | 850 | °C | Performed in vacuum prior to oxidation |
| Max Qutrit Relaxation Rate ($\gamma$) | 240 | kHz | NV5, lowest splitting (10.9 MHz) |
| Typical Qubit Transition Rate ($\Omega$) | 0.17 to 1.85 | kHz | Range observed across measured NVs |
| Shortest $T_{2,max}$ Calculated | 8.3 | ”s | Maximum theoretically achievable coherence time (NV5) |
| Required Magnetic Field ($B_z$) | > 60 | G | Recommended for reduced $\gamma$ and improved $T_{2,max}$ |
| Estimated Electric Field Noise ($E_{RMS}$) | 107 | V/m | Estimated surface noise magnitude |
| Noise Power Spectral Density Scaling | $1/f^2$ | N/A | Observed scaling of $\gamma$ with frequency splitting ($\Delta_{\pm}$) |
| Frequency Splitting Range ($\Delta_{\pm}$) | 10.9 to 1148.4 | MHz | Measured range for NV relaxation analysis |
| NV Selection Criteria | g(2)(0) < 0.5 | N/A | Confirmation of single photon emission |
Key Methodologies
Section titled âKey MethodologiesâThe experimental approach focused on characterizing the spin dynamics of single NV centers in commercial nanodiamonds using high-fidelity microwave control and optical readout.
- Material Preparation & Deposition:
- Starting material was commercial NDs (crushed HPHT diamond) subjected to vacuum annealing (850 °C) and acid oxidation (resulting in a carboxylated surface).
- Nanodiamonds were diluted in deionized (DI) water (10 ”g/mL).
- Poly-vinyl alcohol (PVA, 0.17% concentration) was added to enhance substrate adhesion.
- The solution was spin-coated onto a gridded glass coverslip at 3000 rpm for 20 seconds.
- Measurement Setup:
- Experiments conducted using a room temperature confocal microscope (1.3 NA oil-immersion objective).
- NV centers were optically polarized and read out using 532 nm laser illumination.
- State-selective $\pi$-pulses were driven using two signal generators and controlled via LabRAD software.
- NV Selection and Characterization:
- Emitters were verified as single photons using second-order photon correlation measurements (g(2)(τ) < 0.5).
- Optically Detected Magnetic Resonance (ODMR) was used to select NVs with measurable spin contrast.
- Relaxation Measurement:
- Population dynamics into and out of all three spin states ($|H;0\rangle$, $|H;+1\rangle$, $|H;-1\rangle$) were measured using a combination of nine preparation and readout sequences.
- Relaxation rates ($\gamma$ for qutrit transition, $\Omega$ for qubit transition) were extracted by fitting subtracted population decay curves (FΩ(τ) and Fγ(τ)) to single exponential functions, accounting for microwave $\pi$-pulse infidelities.
- Noise Analysis:
- The dependence of $\gamma$ on the frequency splitting $\Delta_{\pm}$ was characterized to determine the power spectral density scaling ($1/f^2$).
- Temporal fluctuations in $\gamma$ were tracked over hour-to-day timescales, providing evidence that the noise emanates from the nanodiamond surface.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research confirms that diamond qualityâspecifically crystal purity and controlled surface engineeringâis paramount for achieving long coherence times necessary for practical quantum sensing. The commercial materials used introduce debilitating surface charge noise. 6CCVD offers high-specification MPCVD diamond materials and custom engineering services specifically designed to overcome these limitations.
Applicable Materials
Section titled âApplicable MaterialsâThe fast relaxation observed is a direct consequence of the high defect density inherent in HPHT-derived NDs (60-80 ppm N) and the resultant surface strain and charge traps. To replicate or extend this research with maximized quantum performance, researchers require ultra-high purity materials.
| 6CCVD Material Specification | Application in Quantum Sensing | Technical Advantage over Referenced Material |
|---|---|---|
| Electronic Grade SCD (Single Crystal Diamond) | Bulk NV creation, high-fidelity quantum memories, strain control. | Lowest achievable concentration of substitutional nitrogen impurities (< 5 ppb), virtually eliminating background magnetic noise (P1 centers). |
| Optical Grade SCD Wafers | Integrated nanophotonics, maximizing optical coupling and minimizing noise. | SCD wafers up to 125 mm diameter and substrates up to 10 mm thick, polished to Ra < 1 nm for ideal surface engineering. |
| High Purity PCD Wafers | Scalable devices and large-area sensing arrays where single-crystal substrate size is a constraint. | PCD wafers up to 125 mm diameter, offering highly uniform purity and thermal properties. |
Customization Potential
Section titled âCustomization PotentialâThe optimization of NV performance requires precise control over geometry, NV depth, and integration with microwave components. 6CCVDâs specialized services directly enable advanced experimental design:
- Custom Dimensions and Thickness Control:
- 6CCVD provides custom thickness control for SCD/PCD films (0.1 ”m to 500 ”m) and substrates (up to 10 mm). This allows researchers to choose materials suitable for creating shallow NVs (few nm depth) for surface studies or deeply buried NVs to minimize surface electric field noise, enabling operation at lower magnetic fields.
- We offer advanced laser cutting services for precise structuring of wafers to specific geometries required for microwave components or sensing tips.
- Surface and Interface Engineering:
- The paper identifies surface charge noise as the limiting factor. 6CCVD provides ultra-smooth polishing capabilities (Ra < 1 nm for SCD) essential for subsequent low-noise surface passivation (e.g., thermal oxidation) or advanced functionalization that stabilizes the surface charge environment.
- Custom Metalization Capabilities:
- To implement the recommended magnetic field control ($B_z > 60$ G) and future dynamical decoupling sequences, on-diamond microwave structures are necessary. 6CCVD offers in-house deposition of standard and custom metal stacks including Au, Pt, Pd, Ti, W, and Cu for reliable, low-loss microwave strip lines and electrodes.
Engineering Support
Section titled âEngineering SupportâUnderstanding the complex interactions between electric field noise, strain, and material purity requires deep material science expertise. 6CCVD maintains an in-house PhD engineering team available to consult on:
- Material Selection: Assistance in selecting the optimal MPCVD growth parameters (e.g., N or Si concentration) and material type (SCD vs. PCD, high strain vs. low strain) to meet specific quantum application requirements (e.g., maximizing $T_2$ or achieving high NV yield).
- Process Integration: Guidance on post-processing techniques (e.g., annealing recipes, surface treatments) to mitigate surface noise, directly addressing the limitations observed in the current research.
Call to Action: For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We are dedicated to providing the enabling material platform for the next generation of NV-based quantum technologies.
View Original Abstract
Thanks to their versatility, nitrogen-vacancy (N-V) centers in nanodiamonds have been widely adopted as nanoscale sensors. However, their sensitivities are limited by their short coherence times relative to N-Vs in bulk diamond. A more complete understanding of the origins of decoherence in nanodiamonds is critical to improving their performance. Here we present measurements of fast spin relaxation on qutrit transitions between the energy eigenstates composed of the m<sub>s</sub> = | ± 1 $\rangle$ states of the N- V<sup>-</sup> electronic ground state in approximately 40-nm nanodiamonds under ambient conditions. For frequency splittings between these states of 20 MHz or less the maximum theoretically achievable coherence time of the N-V spin is approximately 2 orders of magnitude shorter than would be expected if the N-V spin is treated as a qubit. We attribute this fast relaxation to electric field noise. We observe a strong falloff of the qutrit relaxation rate with the splitting between the states, suggesting that, whenever possible, measurements with N-Vs in nanodiamonds should be performed at moderate axial magnetic fields ( > 60 G). We also observe that the qutrit relaxation rate changes with time. These findings indicate that surface electric field noise is a major source of decoherence for N-V s in nanodiamonds.