Interplay between geometric and dynamic phases in a single-spin system
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-09-23 |
| Journal | Physical review. B./Physical review. B |
| Authors | A. A. Wood, Kirill Streltsov, R. M. Goldblatt, Martin B. Plenio, Lloyd C. L. Hollenberg |
| Institutions | UniversitÀt Ulm, Centre for Quantum Computation and Communication Technology |
| Citations | 6 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Geometric Phases in NV Centers
Section titled âTechnical Documentation & Analysis: Geometric Phases in NV Centersâ6CCVD Material Science Analysis of arXiv:2005.05619v1
Executive Summary
Section titled âExecutive SummaryâThis research paper details the experimental investigation of non-adiabatic Aharonov-Anandan (AA) geometric phases in the ground state triplet of a single Nitrogen-Vacancy (NV) center in diamond. The findings have significant implications for the design of fault-tolerant quantum gates.
- Core Achievement: Successful measurement of the AA geometric phase accumulated during cyclic spin evolution driven by detuned microwave (mw) C-pulses and free precession dynamics.
- Material Requirement: The experiment relies critically on a high-purity, $^{12}$C-enriched CVD diamond substrate, mounted on the (100) face, to achieve long coherence times (T2 $\approx$ 50 ”s, T1 $\approx$ 1 ms).
- Methodology: The total phase is decomposed into dynamic ($\Phi_{dyn}$) and geometric ($\Phi_{AA}$) components, with the global phase detected via reference interferometry using the third spin level (ms = 0 $\leftrightarrow$ ms = -1 transition).
- Key Challenge: The study reveals that in the microwave rotating frame, the AA phase is accompanied by an inseparable dynamic phase, which suppresses the purely geometric dependence of the system dynamics.
- 6CCVD Value Proposition: Replication and extension of this research requires ultra-high purity, low-strain Single Crystal Diamond (SCD) with precise crystal orientation, a core specialization of 6CCVDâs MPCVD growth capabilities.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental setup and results described in the paper:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Material | $^{12}$C-enriched CVD | SCD | Substrate optimized for low noise and long coherence |
| Crystal Orientation | (100) | Face | Mounting orientation for NV axis control |
| Coherence Time (T2) | 50 | ”s | Typical room-temperature performance |
| Relaxation Time (T1) | 1 | ms | Typical room-temperature performance |
| NV Zero-Field Splitting (Dzfs/2$\pi$) | 2.870 | GHz | Intrinsic ground state triplet splitting |
| Gyromagnetic Ratio ($\gamma$/2$\pi$) | 2.8 | MHz G-1 | Zeeman shift constant |
| Bias Magnetic Field (B) | 15 | G | Applied along the surface normal ($\theta$ = 54.7° to NV axis) |
| Microwave Rabi Frequency ($\Omega$) | $\le$ 500 | kHz | Used to minimize off-resonant dressing of hyperfine states |
| Detuning Range ($\Delta$) | $\pm$ 1.0 | MHz | Range used for C-pulse detuning variation |
| Copper Wire Diameter | 20 | ”m | Used for applying microwave fields |
| Copper Wire Distance | 100 | ”m | Distance above diamond surface |
Key Methodologies
Section titled âKey MethodologiesâThe experimental investigation of the geometric and dynamic phase interplay utilized precise control over the NV spin state through a combination of optical and microwave techniques:
- Material Selection and Preparation: A $^{12}$C-enriched CVD diamond was selected and mounted on the (100) face to ensure high isotopic purity, low strain, and optimal NV axis alignment relative to the applied magnetic field.
- Magnetic Field Application: A 15 G magnetic bias field was applied to lift the degeneracy of the ms = $\pm$1 states, enabling individual addressing of the two-level pseudospin subspaces ({0, +1} and {0, -1}).
- Microwave Pulse Generation: Three independently tunable microwave sources were used, gated by fast switches, and applied via a 20 ”m copper wire positioned 100 ”m above the diamond surface. The Rabi frequency ($\Omega$) was kept low ($\le$ 500 kHz).
- Cyclic Evolution (C-Pulses): Detuned microwave pulses (C-pulses) were applied for one Rabi period, $t_{2\pi}(\Delta) = 2\pi / \sqrt{\Omega^{2} + \Delta^{2}}$, driving the spin along a cone trajectory on the Bloch sphere to accumulate the AA phase ($\Phi_{AA}$).
- Nested Interferometry: Complex pulse sequences (e.g., Sequence 1, 2, 3, 4) nested the C-pulse evolution within a resonant Ramsey interferometry sequence. This allowed the global phase accumulated in the driven subspace (e.g., {0, +1}) to be read out as a relative phase shift using the undriven subspace (e.g., {0, -1}) as a reference.
- Phase Characterization: The resulting NV ms = 0 bright state population was measured, varying the C-pulse detuning ($\Delta$) and the cumulative rotation number (N) to characterize the phase shift, which was fitted to the form $\cos^{2}(N\Phi_{T})$.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe demanding requirements of non-adiabatic geometric phase experimentsâspecifically the need for ultra-high purity, low-strain diamond with precise geometry and potential for integrated microwave controlâare perfectly aligned with 6CCVDâs core manufacturing expertise.
| Research Requirement | 6CCVD Solution & Capability | Technical Advantage for Quantum Research |
|---|---|---|
| Ultra-High Purity Substrate ($^{12}$C-enriched, low N) | Optical Grade Single Crystal Diamond (SCD). We specialize in MPCVD growth of SCD with extremely low defect density (N < 5 ppb) and high isotopic enrichment (> 99.999% $^{12}$C). | Guarantees maximum T1 and T2 coherence times (essential for complex, multi-pulse sequences) and minimizes decoherence from spin bath noise. |
| Specific Crystal Orientation ((100) face) | Custom Crystal Orientation and Polishing. We offer SCD wafers grown and polished to specific orientations ((100), (111), (110)) with superior surface roughness (Ra < 1 nm). | Ensures precise alignment of the NV axis relative to external fields, critical for controlled Zeeman splitting and reproducible quantum gate operations. |
| Custom Sample Geometry (Implied small, precise cuts for mw setup) | Custom Dimensions and Laser Machining. We provide SCD plates/wafers up to 125 mm (PCD) and substrates up to 10 mm thick, cut to exact specifications. | Facilitates integration into specialized experimental setups, such as optimizing sample size for high-efficiency coupling to micro-wires or coplanar waveguides. |
| Integrated Microwave Control (Future on-chip striplines) | Advanced Metalization Services. Internal capability for depositing thin films (Au, Pt, Pd, Ti, W, Cu) with high precision lithography. | Enables direct fabrication of on-chip microwave delivery structures, simplifying the setup and improving the fidelity of the C-pulses and Ramsey sequences. |
| Replication & Extension Support | In-House PhD Engineering Support. Our expert team assists with material selection, doping control (e.g., shallow NV creation), and surface termination optimization for quantum applications. | Provides authoritative guidance to accelerate research, ensuring the diamond material properties are perfectly matched to the requirements of geometric phase measurement and fault-tolerant quantum computing projects. |
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).
View Original Abstract
We use a combination of microwave fields and free precession to drive the spin of a nitrogen-vacancy (NV) center in diamond on different trajectories on the Bloch sphere and investigate the physical significance of the frame-dependent decomposition of the total phase into geometric and dynamic parts. The experiments are performed on a two-level subspace of the spin-1 ground state of the NV, where the Aharonov-Anandan geometric phase manifests itself as a global phase, and we use the third level of the NV ground-state triplet to detect it. We show that while the geometric Aharonov-Anandan phase retains its connection to the solid angle swept out by the evolving spin, it is generally accompanied by a dynamic phase that suppresses the geometric dependence of the system dynamics. These results offer insights into the physical significance of frame-dependent geometric phases.