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 | The University of Melbourne, UniversitÀt Ulm |
| Citations | 6 |
| Analysis | Full AI Review Included |
Interplay between Geometric and Dynamic Phases in a Single Spin System
Section titled âInterplay between Geometric and Dynamic Phases in a Single Spin SystemâExecutive Summary
Section titled âExecutive SummaryâThis research investigates the fundamental interplay between geometric (Aharonov-Anandan, AA) and dynamic phases in a single Nitrogen-Vacancy (NV) center spin system, focusing on implications for robust quantum control.
- Core System: Experiments were performed on a single NV center in 12C-enriched CVD diamond, utilizing the spin-1 ground state triplet and addressing two-level pseudospin subspaces using microwave (mw) fields.
- Geometric Phase Detection: The global phase accumulated in the driven two-level subspace was successfully detected using a nested Ramsey interferometry sequence applied to the third, reference level of the spin-1 system.
- Inseparable Phases: For composite, sequential trajectories (Sequences 3 and 4), the geometric phase (related to the solid angle swept on the Bloch sphere) is accompanied by an inseparable dynamic phase in the rotating frame of reference.
- Geometric Invariance: The total measured phase shift for these composite sequences was found to be invariant to geometric manipulations (e.g., varying the ratio of free evolution times T1/T2), demonstrating that the accompanying dynamic phase exactly cancels the geometric dependence.
- Significance: The results reveal that for non-adiabatic, multi-Hamiltonian evolutions, simple geometric arguments alone are insufficient to predict system dynamics, underlining the challenge of isolating the noise-resilient properties of geometric phases in practical solid-state systems.
- Future Direction: The findings motivate further investigation into schemes, such as the Quantum Zeno effect, that may successfully isolate a purely geometric phase component for robust quantum gate implementation.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| NV Host Material | 12C-enriched | CVD Diamond | Sample type |
| NV Ground State | Spin-1 | Triplet | Electronic spin configuration |
| NV Zero-Field Splitting (Dzfs/2Ï) | 2.870 | GHz | Energy gap between ms=0 and ms=±1 |
| Gyromagnetic Ratio (Îł/2Ï) | 2.8 | MHz G-1 | Zeeman shift coefficient |
| Magnetic Bias Field (B) | 15 | G | Applied to break ms=±1 degeneracy |
| Bias Field Angle (ΞB) | 54.7 | ° | Relative to the NV axis |
| Microwave Rabi Frequency (Ω) | †500 | kHz | Used for spin manipulation pulses |
| Microwave Wire Diameter | 20 | ”m | Used for applying mw fields |
| Microwave Wire Distance | 100 | ”m | Distance above the diamond surface |
| Optical Pumping Wavelength | 532 | nm | Used for spin preparation and readout |
| Coherence Time (T2*) | 50 | ”s | Typical room-temperature dephasing time |
| Coherence Time (T2) | 1 | ms | Typical room-temperature coherence time |
| Operating Temperature | Room | Temperature | Experimental condition |
Key Methodologies
Section titled âKey MethodologiesâThe experiment utilized a combination of specialized microwave pulse sequences and reference interferometry on a single NV center in diamond.
- Sample and Setup: A single NV center in a 12C-enriched CVD diamond was optically addressed using a confocal microscope. The diamond was held static, and a 15 G magnetic bias field was applied at 54.7° to the NV axis.
- Microwave Control: Three independent microwave sources were used to generate pulses (Ω †500 kHz), applied via a 20 ”m copper wire. The sources were tuned to the |ms = ±1, mI = 0> hyperfine transitions, ensuring only one two-level subspace was driven at a time.
- C-Pulse Implementation: The fundamental geometric operation, the C-pulse (Cone pulse), was executed by applying a detuned microwave field for one Rabi period (t2Ï). This drives the spin along a cyclic trajectory on the Bloch sphere, sweeping a solid angle (Î) determined by the detuning (Î).
- Reference Interferometry: The NV centerâs spin-1 structure was exploited for phase detection. A resonant Ramsey sequence was applied to a reference subspace (e.g., {0, -1}) to read out the global phase accumulated by the C-pulse sequence applied to the target subspace (e.g., {0, +1}).
- Composite Trajectories: Sequences 3 and 4 involved multiple sequential evolutions, combining C-pulses (driving under a detuned Hamiltonian) with free precession (driving under the static Hamiltonian) in the rotating frame.
- Phase Analysis: The total measured phase (ÏT) was decomposed into dynamic (Ïdyn) and geometric (ÏAA) components using the Aharonov-Anandan formulation, confirming that for composite paths, the dynamic phase cancels the geometric dependence, resulting in a total phase invariant to geometric path changes.
Commercial Applications
Section titled âCommercial ApplicationsâThe fundamental research on geometric phases in NV centers has direct relevance to the development of robust quantum technologies.
- Quantum Computing (Fault Tolerance): Geometric phases are intrinsically resilient to certain types of noise (e.g., timing errors or slow Hamiltonian fluctuations). This work is foundational for engineering robust, fault-tolerant quantum gates (Geometric Quantum Computation) using solid-state spin qubits.
- High-Sensitivity Quantum Sensing: NV centers are premier solid-state magnetometers. Protocols based on geometric phases could lead to magnetometers that are inherently less sensitive to environmental noise (like temperature or strain variations) compared to traditional dynamic phase sensing methods (Ramsey magnetometry).
- Inertial Sensing (Gyroscopes): The paper suggests implementing the scheme to detect the Aharonov-Anandan phase accumulated due to the physical rotation of the NV center. This opens avenues for developing highly sensitive, solid-state quantum gyroscopes.
- Advanced Quantum Control: The precise manipulation of spin trajectories and the understanding of phase accumulation in a complex spin-1 system provide essential knowledge for designing high-fidelity, non-adiabatic control sequences necessary for next-generation quantum hardware.
- Solid-State Qubit Engineering: The use of 12C-enriched CVD diamond confirms the materialâs role as a leading platform for developing stable, room-temperature quantum hardware, supporting the commercialization of diamond-based quantum devices.
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.