Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators

At a Glance

Metadata	Details
Publication Date	2015-06-17
Journal	Physical Review A
Authors	Qian Liu, Mei Zhang
Institutions	Beijing Normal University
Citations	74
Analysis	Full AI Review Included

Technical Documentation & Analysis: Hyperentanglement via NV Centers in MTRs

Document Title: High-Fidelity Quantum Hyperentanglement Generation and Analysis leveraging MPCVD Diamond NV Centers Source Paper: arXiv:1507.06108v1 - Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators

Executive Summary

This research demonstrates highly efficient and deterministic schemes for generating and analyzing hyperentangled quantum states (Bell and GHZ states) using Nitrogen-Vacancy (NV) centers embedded in diamond, coupled to Microtoroidal Resonators (MTRs). This architecture is critical for high-capacity quantum communication.

Key achievements and value propositions include:

Deterministic Generation: Achieved deterministic generation of two-photon polarization-spatial hyperentangled Bell states via controlled Cavity Quantum Electrodynamics (QED) and Faraday rotation induced by the NV center spin state.
Nondestructive Analysis (HBSA): Proposed a complete nondestructive Hyperentangled Bell State Analysis (HBSA) scheme capable of distinguishing all 16 hyperentangled Bell states using four NV-MTR systems and linear optics.
High Fidelity Performance: Calculated fidelities exceed 99% (HBSG) and 99.58% (HBSA) in the strong-coupling regime (g/sqrt{KY} ≥ 3), confirming feasibility with current experimental techniques.
Material Dependence: Success hinges on ultra-high quality diamond substrates supporting NV centers with long electron spin coherence times (T₂ > 10 ms).
Simplified Implementation: Schemes relax experimental difficulties found in previous works, avoiding the need for specific transmission-reflectance balancing in the cavity systems.
Application Potential: Directly benefits long-distance, high-capacity quantum communication applications such as quantum teleportation, dense coding, and quantum repeaters utilizing multiple degrees of freedom (DOFs).

Technical Specifications

The operational success and calculated performance metrics are heavily dependent on achieving strong coupling parameters within the diamond/MTR system.

Parameter	Value	Unit	Context / Condition
Ground State Splitting	2.87	GHz	Between
Electron Spin Coherence Time (T₂)	> 10	ms	Required for sequential photon interaction (Time interval Δt < T₂)
Spin Relaxation Time (T₁)	μs to seconds	N/A	Observed range in diamond NV centers at low temperature
Microcavity Q Factor (Q)	≥ 25000	N/A	Chip-based microcavity minimum value cited for strong coupling
Coupling Strength (g/2π)	0.3 - 1	GHz	Strong coupling regime demonstrated in NV-MTR/Microdisk systems
Ideal Coupling Parameter (g/sqrt{KY})	≥ 3	N/A	Required to achieve F > 99% fidelity for HBSG (excluding F₃)
HBSG Fidelity (F₁, F₂, F₄)	> 99	%	Generation of hyperentangled Bell states (g/sqrt{KY} ≥ 3)
HBSA Fidelity	> 99.58	%	Complete nondestructive analysis (g/sqrt{KY} ≥ 3, κ_s/κ = 0.06)
HBSG Efficiency (η₁)	> 71.75	%	Generation efficiency (g/sqrt{KY} ≥ 3, κ_s/κ = 0.06)
HBSA Efficiency (η)	> 51.48	%	Analysis efficiency (g/sqrt{KY} ≥ 3, κ_s/κ = 0.06)
Phase Shift Requirement	π	N/A	Required phase shift induced by NV-cavity interaction (Faraday rotation)

Key Methodologies

The schemes for hyperentanglement generation (HBSG) and analysis (HBSA) rely on deterministic photon-NV center interactions mediated by Microtoroidal Resonators (MTRs) operating under the principles of Cavity QED.

1. NV Center Preparation

Substrate: High-purity diamond lattice hosting negatively charged Nitrogen-Vacancy (NV^-) centers.
Coupling: NV centers are coupled to MTRs, specifically utilizing the Whispering-Gallery Mode (WGM) of the resonator.
Initialization: NV electron spins are initialized into a superposition state: $|\phi^{+}\rangle = (|-\rangle + |+\rangle) / \sqrt{2}$.

2. Photon-NV Interaction & Phase Shift (Cavity QED)

Resonant Condition: The photon frequency ($\omega$), cavity frequency ($\omega_c$), and atomic transition frequency ($\omega_0$) are matched ($\omega_0 = \omega_c = \omega$).
Input Process: Single, polarized photons (Right/Left Circularly Polarized, |R> / |L>) are successively input into the single-sided cavity.
Faraday Rotation: The spin-selective optical transition rules (via Faraday rotation) dictate that the photon experiences a $\pi$ phase shift depending on the initial spin state of the NV center, achieving the critical transformation summarized in Equation (5):
- $|R\rangle |+\rangle \to |R\rangle |+\rangle$
- $|L\rangle |+\rangle \to -|L\rangle |+\rangle$
- $|R\rangle |-\rangle \to -|R\rangle |-\rangle$
- $|L\rangle |-\rangle \to |L\rangle |-\rangle$

3. Hyperentanglement Generation (HBSG) Steps

Preparation: Two photons (a and b) in identical superposition states are successively injected.
Splitting: Photons pass through a Circular Polarization Beam Splitter (PBS), splitting the polarization (P) DOF into two spatial modes (S) (a₁/a₂, b₁/b₂).
Interaction: The spatial modes interact with two prepared NV centers (NV₁, NV₂).
Mixing: The wave packets are mixed using a standard 50:50 Beam Splitter (BS).
Readout: The polarization-spatial hyperentangled Bell state of the two photons is determined by measuring the final electron spin states of NV₁ and NV₂ (using resonant optical excitation after a Hadamard operation).

4. Nondestructive Analysis (HBSA) Steps

System Scale: Requires four NV-MTR systems (NV₁, NV₂, NV₃, NV₄) and linear optical elements (HWP, QWP, BS).
Sequential Interaction: The entangled photon pair (a, b) passes sequentially through the first two cavities (NV₁, NV₂).
Phase-to-Parity Transformation: Photons pass through BS and a Quarter-Wave Plate (QWP) to transform the acquired phase information into parity discrimination in both polarization and spatial DOFs.
Final Measurement: The photons pass through the remaining NV-cavity systems (NV₃, NV₄). The final hyperentangled Bell state is determined completely and non-destructively by measuring the collective spin states of all four NV centers.

6CCVD Solutions & Capabilities

The successful implementation of this hyperentanglement protocol relies fundamentally on securing diamond substrates of exceptional purity, crystal perfection, and surface quality to maximize the coherence time of the NV centers and facilitate high-Q optical coupling. 6CCVD is uniquely positioned to supply the required materials and custom engineering services.

Applicable Materials

The core requirement is for low-strain, ultra-high purity Single Crystal Diamond (SCD) that minimizes environmental decoherence and supports efficient NV center creation/manipulation.

6CCVD Material Solution	Specification & Role in Research	Customization Notes
Optical Grade Single Crystal Diamond (SCD)	Required for ultra-long NV coherence times (T₂ > 10 ms). Low strain and low native nitrogen content are essential for maximizing system fidelity (F > 99%).	Can be supplied as thin films (0.1 μm) or thick substrates (up to 500 μm) for integration with MTRs or bulk devices.
Isotopically Purified SCD (¹²C enriched)	Recommended to reduce microwave manipulation imperfection and achieve the highest possible coherence times ($T_2$ and $T_1$). Directly referenced in the paper (p. 9) as a route for optimization.	6CCVD offers high-enrichment SCD tailored specifically for advanced solid-state quantum applications.
Ultra-Smooth Polishing (SCD)	Critical for coupling to Microtoroidal Resonators (MTRs) and Whispering-Gallery Modes (WGM). Minimizing scatter loss ensures the high Q factor (> 25000) required for strong coupling (g/sqrt{KY} ≥ 3).	Standard SCD polishing achieves Ra < 1 nm. Custom surface preparations are available for QED interface requirements.
Custom Substrate Thickness	The calculation parameters are based on a strong-coupling system integrating the NV center in the diamond lattice and the MTR. Precise thickness control is necessary for optimizing QED performance.	SCD substrates can be provided with precise thickness control, ranging from 0.1 μm to 500 μm, essential for integrated optics and microcavity fabrication.

Customization Potential

The integration of NV-MTR systems often requires precise geometric features and connection interfaces. 6CCVD provides in-house manufacturing capabilities to meet these complex engineering needs:

Custom Dimensions: While MTRs are chip-scale, 6CCVD provides the necessary wafers and plates up to 125 mm (PCD) and large-area SCD for high-throughput device fabrication.
Advanced Laser Cutting: Our specialized laser cutting services can define precise geometric features, alignment markers, and dicing patterns required for microcavity construction and linear optical component integration (PBS, BS, HWP).
Multi-Layer Metalization: Although not a primary focus of the quantum interaction itself, integrated quantum circuits often require electrical leads or contact pads. 6CCVD offers in-house deposition of standard quantum contact metals including Au, Pt, Pd, Ti, W, and Cu for subsequent device integration.

Engineering Support

Achieving the strong coupling regime (g/sqrt{KY} ≥ 3) and maximizing NV coherence time (T₂ > 10 ms) is a materials challenge. 6CCVD’s in-house PhD team provides expert consultation on material selection, growth recipe optimization, and post-growth processing (such as annealing for NV concentration control) for similar Quantum Information Processing projects. We ensure the diamond characteristics are perfectly matched to the specific demands of high-fidelity, high-efficiency hyperentanglement protocols.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

We present two efficient schemes for the deterministic generation and the complete nondestructive analysis of hyperentangled Bell states in both the polarization and spatial-mode degrees of freedom (DOFs) of two-photon systems, assisted by the nitrogen-vacancy (NV) centers in diamonds coupled to microtoroidal resonators as a result of cavity quantum electrodynamics (QED). With the input-output process of photons, two-photon polarization-spatial hyperentangled Bell states can be generated in a deterministic way and their complete nondestructive analysis can be achieved. These schemes can be generalized to generate and analyze hyperentangled Greenberger-Horne-Zeilinger states of multi-photon systems as well. Compared with previous works, these two schemes relax the difficulty of their implementation in experiment as it is not difficult to obtain the $\pi$ phase shift in single-sided NV-cavity systems. Moreover, our schemes do not require that the transmission for the uncoupled cavity is balanceable with the reflectance for the coupled cavity. Our calculations show that these schemes can reach a high fidelity and efficiency with current technology, which may be a benefit to long-distance high-capacity quantum communication with two DOFs of photon systems.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.91.062321