Level anti-crossings of a nitrogen-vacancy center in diamond - decoherence-free subspaces and 3D sensors of microwave magnetic fields
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-10-01 |
| Journal | New Journal of Physics |
| Authors | K Rama Koteswara Rao, Dieter Suter |
| Citations | 8 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research investigates the exploitation of Energy Level Anti-Crossings (LACs) in a Nitrogen-Vacancy (NV) center coupled to a first-shell Carbon-13 (13C) nuclear spin, yielding significant improvements in quantum coherence and enabling advanced sensing capabilities.
- Decoherence Mitigation: Operating the NV center at specific LAC orientations creates Decoherence-Free Subspaces (DFS), where transitions exhibit ZEro First-Order Zeeman (ZEFOZ) shift, minimizing magnetic field noise perturbations.
- Coherence Enhancement: The coherence time (T2*) of key electron spin transitions was extended by a factor of 5 to 7, reaching up to 10.5 ”s, compared to 1.6 ”s at arbitrary orientations.
- Single-Spin Vector Detection: The LACs cause transition amplitudes to be dominated by a single Cartesian component (x, y, or z) of the magnetic dipole moment, enabling the determination of the full 3D orientation (polar and azimuthal angles) and strength of applied microwave (MW) fields using a single NV center.
- Precision Control: Accurate determination of the MW field orientation (e.g., azimuthal angle η â 45.3°) is critical for implementing high-fidelity numerical optimal control techniques, especially given the broken rotational symmetry caused by the adjacent 13C atom.
- LAC Conditions: Two primary LAC regimes were studied: (i) Zeeman splitting equals 13C hyperfine splitting (B â 28.9 G, Ξ â 38.4°), and (ii) Transverse field orientation (Ξ = 90°).
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Electron Spin Zero-Field Splitting (D) | 2.87 | GHz | Intrinsic NV property. |
| Static Magnetic Field Strength (B) | 28.9 | G | Field used for LAC experiments. |
| 13C Hyperfine Splitting (A1zz) | 128.9 | MHz | Coupling constant along the NV axis. |
| Quadrupolar Splitting (14N, P) | -4.95 | MHz | 14N nuclear spin property. |
| Coherence Time (T2*) (Arbitrary B) | 1.6 (1.3, 1.9) | ”s | Baseline measurement without LAC optimization. |
| Coherence Time (T2*) (LAC Optimized) | 7.6 to 10.5 | ”s | T2* for transitions 1-4 at Ξ â 38.4°. |
| Coherence Enhancement Factor | 5 to 7 | Times | Improvement achieved by operating at LACs. |
| Minimum Line Width (at Ξ = 90°) | 0.12 | MHz | Achieved at the transverse field LAC (5-7x reduction). |
| Detected MW Magnetic Field (Bmw) | 0.31 | G | Determined amplitude using vector detection. |
| Detected RF Magnetic Field (Brf) | 0.12 | G | Determined amplitude using vector detection. |
| Substitutional Nitrogen Concentration | < 5 | ppb | Purity of the diamond crystal used. |
Key Methodologies
Section titled âKey MethodologiesâThe experiments relied on precise control of the static magnetic field orientation and standard optically detected magnetic resonance (ODMR) techniques adapted for coherence measurement.
- System Preparation: A single NV center coupled to a first-shell 13C nuclear spin was isolated in a natural-abundance 13C diamond crystal with low substitutional nitrogen concentration (< 5 ppb).
- MW Field Generation: Microwave (MW) fields were generated using a 20 ”m thin wire attached directly to the diamond surface, integrated into a home-built confocal microscope setup.
- Static Field Control: A permanent magnet was mounted on two rotational stages, allowing for precise 3D rotation and orientation control of the static magnetic field (B = 28.9 G) relative to the NV axis.
- Coherence Measurement (T2*): Free Induction Decays (FIDs) were measured using the Ramsey pulse sequence (Laser Initialization, MW Ï/2 pulse, delay Ï, MW Ï/2 pulse, Readout).
- Spectral Analysis: FIDs were Fourier transformed to obtain Electron Spin Resonance (ESR) spectra. Coherence times (T2) were quantified by inverse Fourier transforming selected spectral lines and fitting the decay to $a \cos(2\pi \nu t) \exp(-t/T_{2}^{})$.
- Vector Detection: The azimuthal angle (η) of the MW field was determined by comparing the amplitudes (Ia) of the four primary transitions (I1/I2 = I3/I4 = |tan η|). The polar angle (ζ) was determined by comparing the Rabi frequencies of transitions excited by the y-component (MW) versus the z-component (RF) of the respective fields.
Commercial Applications
Section titled âCommercial ApplicationsâThe demonstrated ability to achieve long coherence times and perform single-spin vector magnetometry is highly relevant for emerging quantum technologies.
| Industry/Field | Application/Product Relevance |
|---|---|
| Quantum Computing & Qubit Control | The NV-13C system serves as a robust, long-coherence qubit register. DFS operation ensures stability, while precise MW field vector detection is essential for implementing high-fidelity, fast multi-qubit gates via optimal control sequences. |
| Microwave Magnetometry | Enables single-spin 3D vector detection of MW magnetic fields. This is critical for characterizing complex electromagnetic environments, testing integrated circuits (ICs), and performing nano-scale imaging of current flows. |
| Quantum Sensing (Robustness) | The use of LACs and ZEFOZ shifts provides intrinsic noise immunity, making NV sensors significantly more robust against environmental magnetic field fluctuations, improving the signal-to-noise ratio in practical sensing applications. |
| Diamond Device Engineering | Requires high-purity diamond substrates with controlled isotopic enrichment (e.g., 12C enrichment to minimize background noise, or specific 13C placement for targeted qubit coupling). |
| Fundamental Physics Research | Provides a platform for studying strong-driving dynamics and quantum systems beyond the rotating-wave approximation, leveraging the long coherence times achieved at the LACs. |
View Original Abstract
Abstract Nitrogen-vacancy (NV) centers in diamond have become an important tool for quantum technologies. All of these applications rely on long coherence times of electron and nuclear spins associated with these centers. Here, we study the energy level anti-crossings of an NV center in diamond coupled to a first-shell 13 C nuclear spin in a small static magnetic field. These level anti-crossings (LACs) occur for specific orientations of the static magnetic field due to the strong non-secular components of the Hamiltonian. At these orientations we observe decoherence-free subspaces, where the electron spin coherence times ( <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ display=âinlineâ overflow=âscrollâ> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> ) are 5-7 times longer than those at other orientations. Another interesting property at these LACs is that individual transition amplitudes are dominated by a single component of the magnetic dipole moment. Accordingly, this can be used for vector detection of microwave magnetic fields with a single NV center. This is particularly important to precisely control the center using numerical optimal control techniques.