Determination of the Three-Dimensional Magnetic Field Vector Orientation with Nitrogen Vacany Centers in Diamond
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-03-17 |
| Journal | Nano Letters |
| Authors | Timo Weggler, Christian Ganslmayer, Florian Frank, Tobias Eilert, Fedor Jelezko |
| Institutions | UniversitÀt Ulm, Center for Integrated Quantum Science and Technology |
| Citations | 33 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive Summaryâ- 3D Vector Magnetometry: The research successfully demonstrates the reconstruction of the absolute 3D orientation (polar and azimuthal angles) of an arbitrary static magnetic field using individual Nitrogen Vacancy (NV) centers in diamond.
- Symmetry Breaking: The technique overcomes the inherent C3v symmetry limitation of single NV centers by combining data derived from pulsed Optically Detected Magnetic Resonance (ODMR) measurements across multiple NV orientations (tetrahedral axes).
- High Precision: The method achieves high angular resolution, determining the B-field vector orientation with an overall error interval of less than 0.4°.
- Methodology: The 3D vector is calculated by determining the tilt angle (Ξi) for three different NV axes, which defines the intersection of three magnetic field cones in a unit sphere model.
- General Applicability: The approach is robust, relying on a simple confocal setup, and does not require special prerequisites like strongly coupled nuclear spins or cryogenic temperatures.
- Core Components: The experimental setup integrates a home-built confocal microscope, high-precision magnet positioning stages, and a pulsed microwave system for spin manipulation.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Magnetic Field Amplitude | ~230 | Gauss | Applied static B-field magnitude |
| Angular Precision (Error) | < 0.4 | ° | Overall error interval for 3D vector reconstruction |
| Zero Field Splitting (D) | 2870 | MHz | NV ground state transition ( |
| Diamond Type | Single-crystal electronic grade | N/A | Element Six, (100) cut |
| Nitrogen Concentration | < 5 | ppb | Substitutional N impurities |
| Boron Concentration | < 1 | ppb | Boron impurities |
| Diamond Height | 35 | ”m | Thickness of laser-cut and polished sample |
| N Implantation Energy | 5 | keV | Used to create NV centers in 12C enriched layer |
| Excitation Wavelength | 519 | nm | Laser diode system (TOPTICA iBeam-Smart-PO) |
| Detection Filter Cut-off | 635 | nm | Long-pass filter for NV fluorescence detection |
| Objective Numerical Aperture (NA) | 1.45 | N/A | Nikon CFI A-Apo 100x oil objective |
| Rabi Period (Ω) | 1.58 | ”s | Used during ODMR measurements (Fig. 3) |
| Typical Measurement Duration | ~1 | hour | Time required for B-field vector reconstruction |
| Magnet Positioning Repeatability | 0.5 | ”m | Achieved using PI miCos translation stages |
| Microwave Antenna Diameter | 25 | ”m | Copper wire used for MW delivery |
Key Methodologies
Section titled âKey Methodologiesâ- Sample Preparation: A single-crystal electronic grade diamond (100) surface was prepared. NV centers were created by 5 keV nitrogen implantation into a chemical vapor deposition (CVD) grown 12C enriched layer.
- Confocal Microscopy Setup: A home-built confocal microscope was used for single NV detection and manipulation, employing a 519 nm pulsed laser for excitation and a 635 nm long-pass filter for photoluminescence (PL) collection.
- Magnetic Field Application: A homogenous static magnetic field (~230 Gauss) was generated using cubic neodymium magnets, precisely positioned using three linear and one rotation stage.
- Microwave (MW) Control: MW pulses were generated using an arbitrary waveform generator (AWG) and amplifier, delivered via a 25 ”m diameter copper wire antenna placed ~15 ”m from the measured NV centers.
- NV Axis Differentiation: Photoluminescence anisotropy measurements (rotating a λ/2-plate) were used to distinguish the four possible NV directions into two orthogonal polarization pairs.
- Tilt Angle Measurement (ODMR): Pulsed ODMR was performed on individual NV centers (NV1, NV2, NV3) to measure the transition frequencies (|0> â |±1>). The symmetry of these transitions relative to the Zero Field Splitting (ZFS) was used to calculate the tilt angle (Ξi) between the NV axis and the B-field vector.
- 3D Vector Reconstruction: The measured tilt angles (Ξi) from three different NV axes were used to define three intersecting cones on a unit sphere. The intersection point provides the B-field vector B = (Bx, By, Bz)T by solving a system of three linear equations, normalized by the condition |B| = 1.
- Error Quantification: The angular covariance matrix was calculated using a bivariate normal distribution model, simulating one million samples to determine the expectation value and standard deviation (Ï) of the resulting B-field orientation.
Commercial Applications
Section titled âCommercial Applicationsâ- Quantum Sensing and Metrology: Provides absolute directional knowledge of magnetic fields, crucial for high-precision quantum magnetometry and spin sensing at the nanometer level.
- Spin-Based Quantum Computation: Essential for controlling and manipulating individual electron spins, where precise knowledge of the local magnetic field orientation is required for gate operations.
- Nanoscale NMR and EPR: Enables new paths for precise Nuclear Magnetic Resonance (NMR) reconstructions and modulation of Electron Paramagnetic Resonance (EPR) measurements by tailoring magnetic fields.
- Vector Magnetic Field Microscopy: Applicable in developing advanced vector magnetometers for probing condensed matter physics and magnetic imaging of biological systems (e.g., living cells).
- Atomic Structure Characterization: The technique can be used to determine the absolute NV-center axis orientation in the diamond lattice, providing atomic structure information via macroscopic measurements.
- Experimental Calibration: The measurement serves as a universal calibration tool to characterize the magnetic field at the focus of a microscope sample for other non-NV based experiments.
View Original Abstract
Absolute knowledge about the magnetic field orientation plays a crucial role in single spin-based quantum magnetometry and the application toward spin-based quantum computation. In this paper, we reconstruct the three-dimensional orientation of an arbitrary static magnetic field with individual nitrogen vacancy (NV) centers in diamond. We determine the polar and the azimuthal angle of the magnetic field orientation relative to the diamond lattice. Therefore, we use information from the photoluminescence anisotropy of the NV, together with a simple pulsed optically detected magnetic resonance experiment. Our nanoscopic magnetic field determination is generally applicable and does not rely on special prerequisites such as strongly coupled nuclear spins or particular controllable fields. Hence, our presented results open up new paths for precise NMR reconstructions and the modulation of the electron-electron spin interaction in EPR measurements by specifically tailored magnetic fields.