Dynamically Encircling an Exceptional Point in a Real Quantum System
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-04-30 |
| Journal | Physical Review Letters |
| Authors | Wenquan Liu, Yang Wu, ChangâKui Duan, Xing Rong, Jiangfeng Du |
| Institutions | Hefei National Center for Physical Sciences at Nanoscale, CAS Key Laboratory of Urban Pollutant Conversion |
| Citations | 126 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Dynamic Exceptional Points in NV Diamond
Section titled âTechnical Documentation & Analysis: Dynamic Exceptional Points in NV Diamondâ6CCVD Material Analysis Reference: Liu et al., Dynamically encircling an exceptional point in a real quantum system (arXiv:2002.06798v1)
Executive Summary
Section titled âExecutive SummaryâThis research successfully demonstrates the dynamic encircling of an Exceptional Point (EP) using a single Nitrogen-Vacancy (NV) center embedded in diamond. This work is highly relevant to quantum sensing and non-Hermitian quantum mechanics, relying critically on high-coherence diamond material.
- Core Achievement: Experimental realization of dynamic EP encircling in a single-spin quantum system, observing both asymmetric and symmetric mode switching.
- Material Requirement: The experiment utilized isotopically purified bulk diamond ($^{12}$C = 99.9%) with a [100] face orientation to host the NV center.
- Coherence Benchmark: A long electron spin dephasing time ($T_2 = 36(3)$ ”s) was achieved, essential for maintaining quantum coherence throughout the 15 ”s encircling process.
- Methodology: The time-dependent non-Hermitian Hamiltonian was engineered using a dilation method, implemented via two selective microwave (MW) pulses.
- Fidelity: High average state fidelities (up to $F_{\rho|\psi\rangle} = 1.00(4)$) validate the experimental control and agreement with theoretical predictions.
- Future Impact: The successful engineering of time-dependent non-Hermitian Hamiltonians opens pathways for robust quantum control and investigation of non-Hermitian topological invariants.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental setup and results, highlighting the critical material and operational parameters.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Material Type | Single Crystal Diamond (SCD) | N/A | Bulk, [100] face. |
| Isotopic Purity ($^{12}$C) | 99.9 | % | Required for high coherence. |
| Electron Spin Dephasing Time ($T_2$) | 36(3) | ”s | Measured via Ramsey experiment. |
| Static Magnetic Field ($B_0$) | 500 | Gauss | Applied along the NV symmetry axis for polarization. |
| Zero-Field Splitting (D) | 2.87 | GHz | Intrinsic property of the NV electron spin. |
| Hyperfine Coupling (A) | -2.16 | MHz | Coupling between electron spin and nuclear spin. |
| Total Encircling Time (T) | 15 | ”s | Duration of the dynamic EP encirclement. |
| Encircling Rate ($\omega$) | $\pm 2\pi / 15$ | rad $\cdot$ ”s-1 | Angular rotation rate in parameter space. |
| Average State Fidelity ($F_{\rho | \psi\rangle}$) | 1.00(4) | N/A |
| Excitation Wavelength | 532 | nm | Green laser used for optical pumping. |
| Objective Numerical Aperture (NA) | 1.42 | N/A | Oil immersion objective used for focusing/collection. |
Key Methodologies
Section titled âKey MethodologiesâThe experiment relies on precise material preparation and advanced quantum control techniques within an optically detected magnetic resonance (ODMR) setup.
- Material Preparation: Use of isotopically purified bulk SCD ([100] face, $^{12}$C = 99.9%) to minimize decoherence sources and maximize the electron spin $T_2$.
- Initialization: The NV center is polarized to the state $|0\rangle_e|1\rangle_n$ using optical pumping (532 nm laser) under a 500 Gauss static magnetic field aligned with the NV axis.
- Qubit Encoding: The electron spin is chosen as the system qubit, and the $^{14}$N nuclear spin is chosen as the ancilla qubit, forming a two-qubit system within the subspace spanned by four specific hyperfine energy levels.
- Hamiltonian Construction: The dilated Hermitian Hamiltonian $H_{s,a}(t)$ is constructed in the NV center subspace by applying two selective, frequency-detuned microwave (MW) pulses.
- Dynamic Evolution: The system evolves under $H_{s,a}(t)$ for a total encircling time of $T = 15$ ”s, realizing the dynamic encircling of the EP in the non-Hermitian system $H_s(t)$.
- State Tomography: Quantum state tomography is implemented by measuring the intermediate state $|\chi(t)\rangle$ (when the ancilla qubit is $|0\rangle$) using photoluminescence (PL) rate differences, followed by maximum likelihood estimation to obtain the final state $|\psi(t)\rangle$.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe successful replication and extension of this high-impact quantum research depend entirely on access to ultra-high-purity, high-coherence diamond materials. 6CCVD is uniquely positioned to supply the necessary Single Crystal Diamond (SCD) substrates.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate the $T_2$ coherence times reported (36 ”s) and push towards longer coherence for more complex quantum protocols, researchers require diamond with superior isotopic purity and minimal defects.
| Research Requirement | 6CCVD Solution | Material Specification |
|---|---|---|
| High Coherence | Quantum Grade Single Crystal Diamond (SCD) | SCD with ultra-low nitrogen content (< 1 ppb) and high isotopic enrichment ($^{12}$C > 99.99%). |
| Bulk Substrate | Custom SCD Substrates | SCD substrates up to 10 mm thickness, ideal for bulk NV center experiments requiring deep focusing or robust handling. |
| Orientation Control | Precision [100] SCD Plates | Guaranteed crystal orientation ([100] face) crucial for aligning the NV symmetry axis with the external magnetic field. |
Customization Potential
Section titled âCustomization Potentialâ6CCVDâs advanced MPCVD growth and post-processing capabilities directly address the needs of quantum engineers working on NV center systems.
- Custom Dimensions and Thickness: While the paper used bulk diamond, 6CCVD can supply SCD plates ranging from 0.1 ”m to 500 ”m thickness, or custom substrates up to 10 mm. We offer plates/wafers up to 125 mm (PCD) for scaling up quantum device fabrication.
- Surface Quality: The use of an oil immersion objective (NA 1.42) demands exceptional surface flatness. 6CCVD guarantees ultra-smooth polishing with Ra < 1 nm on SCD, ensuring optimal optical coupling and minimizing surface-related decoherence.
- Integrated Control Structures: For future integrated quantum devices that move beyond external coils, 6CCVD offers in-house custom metalization services, including deposition of Au, Pt, Pd, Ti, W, and Cu, suitable for fabricating on-chip microwave and RF control lines.
- Laser Processing: We provide precision laser cutting and shaping services to meet unique dimensional requirements for integration into complex ODMR or cryogenic setups.
Engineering Support
Section titled âEngineering SupportâThe successful demonstration of dynamic EP encircling is a significant step in quantum information processing. 6CCVDâs in-house PhD team specializes in the material science of quantum defects and can assist researchers in selecting the optimal diamond grade and processing recipe for similar Non-Hermitian Quantum Dynamics projects. We ensure that the material properties (purity, orientation, and surface finish) are perfectly matched to the demanding requirements of high-fidelity quantum control.
Call to Action: For custom specifications or material consultation regarding Quantum Grade SCD for NV center research, visit 6ccvd.com or contact our engineering team directly. We offer global shipping (DDU default, DDP available) to accelerate your research timeline.
View Original Abstract
The exceptional point, known as the non-Hermitian degeneracy, has special topological structure, leading to various counterintuitive phenomena and novel applications, which are refreshing our cognition of quantum physics. One particularly intriguing behavior is the mode switch phenomenon induced by dynamically encircling an exceptional point in the parameter space. While these mode switches have been explored in classical systems, the experimental investigation in the quantum regime remains elusive due to the difficulty of constructing time-dependent non-Hermitian Hamiltonians in a real quantum system. Here we experimentally demonstrate dynamically encircling the exceptional point with a single nitrogen-vacancy center in diamond. The time-dependent non-Hermitian Hamiltonians are realized utilizing a dilation method. Both the asymmetric and symmetric mode switches have been observed. Our Letter reveals the topological structure of the exceptional point and paves the way to comprehensively explore the exotic properties of non-Hermitian Hamiltonians in the quantum regime.