Conversion of entangled states with nitrogen-vacancy centers coupled to microtoroidal resonators
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2017-06-27 |
| Journal | Optics Express |
| Authors | YanâQiang Ji, XiaoâQiang Shao, X. X. Yi |
| Institutions | Northeast Normal University |
| Citations | 6 |
| Analysis | Full AI Review Included |
Technical Documentation and Analysis: High-Fidelity Entanglement Conversion using N-V Centers in MPCVD Diamond
Section titled âTechnical Documentation and Analysis: High-Fidelity Entanglement Conversion using N-V Centers in MPCVD DiamondâThis document analyzes the research detailing the conversion of entangled GHZ states to W/Dicke states using Nitrogen-Vacancy (N-V) centers coupled to microtoroidal resonators (MTR). The proposed schemes require ultra-high-quality diamond material for realizing deterministic quantum gates, directly aligning with 6CCVDâs specialized capabilities in custom MPCVD Single Crystal Diamond (SCD) platforms.
Executive Summary
Section titled âExecutive SummaryâThe following points summarize the core technical achievement and the role of high-purity diamond in enabling this advanced quantum information processing (QIP) scheme:
- Entanglement Conversion: Efficient schemes are proposed for locally converting multi-photon GHZ states (three, four, and five-photon) into robust W or Dicke entangled states, critical resources for diverse QIP tasks.
- Core Technology: The conversion relies on deterministic CNOT gates built using diamond N-V centers coupled to microtoroidal resonators (MTRs), utilizing single-photon input-output processes and cross-Kerr nonlinearities (CKN).
- High Fidelity Achieved: Theoretical analysis confirms that high-fidelity CNOT gates (Fidelity > 99.5%) are feasible using current experimental parameters for hybrid diamond systems (e.g., diamond-GaP microdisks).
- Deterministic Four-Photon Conversion: The scheme for converting a four-photon GHZ state to a W state achieves unit success probability (100%) without requiring iterative processing.
- Material Imperative: Successful implementation requires high-purity, low-strain diamond substrates (SCD) to ensure long N-V center coherence times ($\gamma_{total}$) and optimize coupling strength ($g/\kappa$ and $g/\gamma$) for robust gate operation.
- Feasibility Confirmed: The error probability for the necessary X homodyne measurement, even with weak cross-Kerr nonlinearities generated in diamond photonic crystal waveguides, is calculated to be less than 10-5, confirming experimental feasibility.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard parameters define the performance and system requirements extracted from the feasibility analysis:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Material System | Hybrid Diamond-GaP | N/A | Proposed microdisk system parameters [61] |
| **CNOT Fidelity (Measurement | +>)** | 99.6% | % |
| **CNOT Fidelity (Measurement | ->)** | 99.5% | % |
| Conversion Success Probability (3-photon GHZ to W) | 99.6% | % | Total success probability after 4 iterations (n=4) |
| Conversion Success Probability (4-photon GHZ to W) | Unit (100%) | % | Deterministic conversion, no iteration required |
| Conversion Fidelity (3-photon GHZ to W, n=4) | 95.7% | % | Overall fidelity considering two CNOT gates |
| Coupling Strength Condition | $g^2$ $\geq$ 25$\kappa\gamma$ | N/A | Required for optimal reflection coefficient $r(\omega_p) = 1$ |
| Probe Photon Number ($a^2$) | 1.3 x 104 | Photons | Required for sufficient cross-Kerr nonlinearity (CKN) |
| N-V Color Center Density (CKN Medium) | 2 x 104 | Centers | Used in cryogenic N-V-diamond system for CKN |
| Required Phase Shift ($\theta$) | > 0.1 | Radian | Minimum shift generated per signal photon for CKN |
| X Homodyne Measurement Error | < 10-5 | N/A | Error probability for distinguishing phase shifts |
Key Methodologies
Section titled âKey MethodologiesâThe conversion schemes rely on specific physical components and sequence operations utilizing the N-V center in diamond:
-
Diamond Platform Integration:
- N-V centers are fabricated and confined close to the surface of a Microtoroidal Resonator (MTR) or embedded in a diamond thin-film photonic crystal waveguide.
- The N-V center ground state $|^3\text{A}, m_s = 0\rangle$ is split into auxiliary levels ($|- \rangle$ and $|+ \rangle$) via Zeeman splitting from an external magnetic field.
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Resonant Coupling for CNOT:
- The N-V center transition between levels ($|- \rangle$ or $|+ \rangle$) and the auxiliary excited state $|e \rangle$ is resonantly coupled to left-circularly polarized ($|L \rangle$) or right-circularly polarized ($|R \rangle$) photons within the MTR.
- Optimal coupling is achieved when the condition $g^2 \geq 25\kappa\gamma$ is met, ensuring a specific phase shift ($\pi$) on the photon output path dependent on the N-V center state.
-
Deterministic CNOT Gate Implementation:
- Photons 1 (target) and 2 (control) pass sequentially through the MTR/N-V setup, controlled by quarter-wave plates (QWP) and optical switches (SW).
- A Hadamard gate (via a $\pi/2$ microwave pulse) is applied to the N-V center before and after interaction with the second photon.
- Measurement of the N-V center state ($|+ \rangle$ or $|- \rangle$) after the process is unequivocally associated with the desired CNOT operation on the two photons.
-
Entanglement Conversion via Cross-Kerr Nonlinearity (CKN):
- The partially converted entangled state interacts with a coherent probe beam in a CKN medium (e.g., a diamond photonic crystal waveguide containing N-V centers).
- The Hamiltonian for CKN ($H = \hbar \chi a_s^\dagger a_s a_p^\dagger a_p$) causes the coherent probe beam to pick up a phase shift ($\theta$) directly proportional to the number of photons present in the entangled state component.
-
State Discrimination:
- A general X Homodyne measurement is performed on the probe beam to distinguish the different acquired phase shifts (e.g., $\theta$, $3\theta$, $5\theta$). These distinctions project the photonic system into the desired W or Dicke state.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research highlights the absolute necessity of integrating high-quality diamond material with complex photonic structures. 6CCVD is uniquely positioned to supply the foundational diamond platforms and engineering services required to replicate or advance these results.
Applicable Materials
Section titled âApplicable MaterialsâTo achieve the necessary N-V center coherence and coupling efficiency, Electronic Grade Single Crystal Diamond (SCD) is essential.
| Research Requirement | 6CCVD Solution | Technical Rationale |
|---|---|---|
| Low N-V Center Decay Rate ($\gamma$) | High-Purity SCD (0.1”m - 500”m) | Electronic grade material minimizes nitrogen concentration and strain, maximizing coherence time (low $\gamma_{total}$) crucial for maintaining high gate fidelity (F > 99.5%). |
| Integration/Waveguides | Custom Thin-Film SCD Substrates | The CKN medium requires diamond thin films/photonic crystal waveguides. We offer SCD in highly controllable thicknesses from 0.1”m up to 500”m. |
| Robust SCD Substrates | Plates/Wafers up to 125mm | Provides a scalable platform for large-scale fabrication of MTR or photonic crystal arrays, moving beyond proof-of-concept size. |
Customization Potential
Section titled âCustomization PotentialâReplicating the experimental setup requires extreme precision in both dimensions and surface properties for efficient MTR or waveguide coupling.
| Custom Service | Application to Research Requirements |
|---|---|
| Precision Polishing (Ra < 1nm SCD) | Required for fabricating high-Q Microtoroidal Resonators or low-loss photonic crystal waveguides on the diamond surface. Surface roughness must be minimized to support coupling. |
| Custom Laser Micromachining | Essential for dicing wafers, creating mounting features, or forming specific diamond geometries required for photonic crystal structures and MTR coupling interfaces. |
| In-House Metalization (Ti, Pt, Au, etc.) | The implementation of $\pi/2$ microwave pulses (for Hadamard gates) and thermal management systems typically requires precise metallic contacts/electrodes. 6CCVD provides custom metal deposition services. |
| Global Logistics Support | We ensure reliable, globally shipped supply (DDU default, DDP available) of specialized SCD substrates, minimizing delay in critical QIP development pipelines. |
Engineering Support
Section titled âEngineering SupportâThe successful implementation of N-V based quantum gates relies heavily on minimizing material imperfections that contribute to decoherence ($\gamma$). Our in-house PhD material science team specializes in tailoring MPCVD growth recipes to optimize diamond purity and strain for solid-state quantum applications.
6CCVDâs expert staff can assist with:
- Material Selection: Determining the optimal SCD thickness and orientation for high-Q resonant coupling structures.
- Surface Preparation Protocols: Providing substrates with guaranteed surface roughness (Ra < 1nm) necessary for subsequent lithography and fabrication steps (ion implantation, etching for N-V based quantum computing projects).
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
We propose efficient schemes for converting three-photon, four-photon and five-photon GHZ state to a W state or Dicke state, respectively with the nitrogen-vacancy (N-V) centers via single-photon input-output process and cross-Kerr nonlinearities. The total success probability can be improved by iterating the conversion process for the case of three-photon and five-photon while it does not require iteration for converting four-photon GHZ state to a W state. The analysis of feasibility shows that our scheme is feasible for current experimental technology.