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Long-range quantum entanglement in dielectric mu-near-zero metamaterials

MetadataDetails
Publication Date2025-09-03
JournalLight Science & Applications
AuthorsOlivia Mello, Larissa Vertchenko, Seth Nelson, Adrien Debacq, Durdu Ö. GĂŒney
InstitutionsMichigan Technological University, Harvard University
AnalysisFull AI Review Included

Technical Documentation & Analysis: Long-Range Quantum Entanglement in Dielectric MNZ Metamaterials

Section titled “Technical Documentation & Analysis: Long-Range Quantum Entanglement in Dielectric MNZ Metamaterials”

This research demonstrates a significant breakthrough in on-chip quantum information processing by achieving robust, long-range quantum entanglement using a fully dielectric Mu-Near-Zero (MNZ) metamaterial platform.

  • Core Achievement: Sustained high-degree quantum entanglement (concurrence) over 17 free-space wavelengths ($\lambda_0$), equivalent to approximately 12.5 ”m, between two distant quantum emitters.
  • Performance Metric: This range represents an order of magnitude improvement over previously proposed plasmonic Epsilon-Near-Zero (ENZ) waveguide systems, while maintaining low intrinsic loss.
  • Material Platform: The system utilizes Silicon Vacancy (SiV) centers embedded in a 2D square lattice of high-purity diamond pillars (n = 2.4064).
  • Mechanism: The MNZ structure effectively drives the refractive index ($n_{eff}$) close to zero at the SiV Zero-Phonon Line (ZPL) of 737 nm, enabling cooperative spontaneous emission over large spatial separations.
  • Design Robustness: Simulations confirm the near-zero index behavior is maintained even under significant fabrication uncertainties (pillar radius perturbations up to $\pm$5 nm).
  • Quantum Signature: The system exhibits a strong antibunching signature (zero time delay second-order correlation function $g^{(2)}(0) \approx 0$) correlated with maximum steady-state concurrence.
  • 6CCVD Value Proposition: This work validates the critical need for high-purity, low-loss Single Crystal Diamond (SCD) substrates, which 6CCVD supplies with custom dimensions, superior polishing (Ra < 1nm), and integrated metalization capabilities for advanced quantum device fabrication.

The following hard data points were extracted from the analysis of the MNZ metamaterial and quantum dynamics:

ParameterValueUnitContext
Target Wavelength ($\lambda_0$)737nmZero-Phonon Line (ZPL) of SiV centers
Entanglement Range (Spatial)17$\lambda_0$Equivalent to approximately 12.5 ”m
Maximum Transient Concurrence ($C$)$\approx$ 0.35DimensionlessSustained over 17 $\lambda_0$ separation
Minimum Effective Refractive Index ($n_{eff}$)-0.03DimensionlessAchieved at 737 nm (MNZ crossing)
Effective Impedance ($Z$)$\approx$ 0.2DimensionlessLow impedance for efficient coupling
Peak Purcell Factor ($F_P$)$\approx$ 7DimensionlessEnhancement near 737 nm
Diamond Refractive Index ($n$)2.4064DimensionlessMaterial used for MNZ pillars
Metamaterial Pitch ($a$)505nm2D square lattice periodicity
Pillar Radius ($r$)115nmDiamond pillar dimension
Second-Order Correlation Function ($g^{(2)}(0)$)$\approx$ 0DimensionlessCorrelated with maximum steady-state concurrence (Antibunching)
Fabrication Tolerance (Radius)$\pm$5nmRobustness demonstrated for $n_{eff}$ near zero

The theoretical and numerical investigation relied on precise material parameters and advanced quantum modeling techniques:

  1. Material Selection and Emitter Integration: High-purity diamond (n = 2.4064) was selected as the host material for Silicon Vacancy (SiV) quantum emitters, targeting the 737 nm ZPL.
  2. MNZ Metamaterial Design: A planar 2D square lattice structure was designed with a pitch ($a$) of 505 nm and a pillar radius ($r$) of 115 nm to achieve the $\mu$-near-zero condition at the target wavelength.
  3. Parameter Retrieval: Full-wave numerical simulations (COMSOL Multiphysics) were used to calculate the effective constitutive parameters ($\epsilon_r$, $\mu_r$) and the effective refractive index ($n_{eff}$) via the transfer matrix method.
  4. Coupling Coefficient Calculation: The cooperative decay rate ($\Gamma_{12}$) and dipole-dipole coupling ($g_{12}$) were determined by sweeping a magnetic dipole source across the MNZ structure up to 25 pitches (12.5 ”m).
  5. Quantum Dynamics Modeling: The quantum dynamics of the two-qubit system were solved using the Lindblad master equation, incorporating the calculated coupling coefficients and decay rates.
  6. Entanglement Quantification: Transient and steady-state concurrence ($C$) were calculated from the density matrix solutions, demonstrating entanglement persistence and spatial range.
  7. Steady-State Analysis: An external pump source was introduced to achieve steady-state entanglement, revealing maximum concurrence under antisymmetric pumping configurations.

This research highlights the critical role of high-quality, custom-engineered diamond materials for realizing next-generation quantum platforms. 6CCVD is uniquely positioned to supply the necessary materials and fabrication support to replicate and extend this long-range entanglement work.

Research Requirement6CCVD Solution & CapabilityTechnical Advantage for Quantum Applications
High-Purity Emitter HostOptical Grade Single Crystal Diamond (SCD)SCD material offers the lowest defect density, crucial for minimizing decoherence and maximizing the stability of implanted SiV centers (ZPL 737 nm).
Custom Substrate DimensionsPlates/Wafers up to 125mm (PCD) / Substrates up to 10mm (SCD)We provide custom-sized SCD substrates necessary for large-area MNZ array fabrication, supporting scaling beyond the 51 $\times$ 51 pitch design demonstrated.
Precise Thickness ControlSCD Thickness: 0.1”m - 500”mWe supply ultra-thin SCD films (0.1”m) for suspended membrane structures or thicker substrates (up to 500”m) for bulk etching, enabling optimal MNZ pillar geometry and waveguide integration.
Surface Quality for NanofabricationSuperior Polishing (Ra < 1nm for SCD)Our industry-leading polishing ensures an atomically smooth surface (Ra < 1nm), essential for high-fidelity electron beam lithography and minimizing optical scattering losses in the 737 nm regime.
Integrated Photonic CircuitryIn-House Custom Metalization (Au, Pt, Ti, W, Cu)We offer internal metal deposition services, allowing researchers to integrate necessary components like pump/output waveguides, electrical contacts, or thermal management layers directly onto the diamond substrate.
Alternative Emitter PlatformsBoron-Doped Diamond (BDD)For experiments requiring conductive substrates or specific electrochemical properties, we offer BDD films, which can be tailored for various quantum sensing or electro-optic applications.
Global Supply Chain ReliabilityGlobal Shipping (DDU default, DDP available)We ensure reliable, timely delivery of sensitive diamond materials worldwide, supporting international research collaborations.

6CCVD’s in-house PhD team specializes in MPCVD diamond growth and material science for quantum applications. We can assist researchers in optimizing material selection (e.g., nitrogen concentration control for NV/SiV yield) and substrate preparation for similar long-range quantum entanglement projects.

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

View Original Abstract

Abstract Entanglement is paramount in quantum information processing. Many quantum systems suffer from spatial decoherence in distances over a wavelength and cannot be sustained over short time periods due to dissipation. However, long range solutions are required for the development of quantum information processing on chip. Photonic reservoirs mediating the interactions between qubits and their environment are suggested. Recent research takes advantage of extended wavelength inside near-zero refractive index media to solve the long-range problem along with less sensitivity on the position of quantum emitters. However, those recent proposals use plasmonic epsilon near-zero waveguides that are intrinsically lossy. Here, we propose a fully dielectric platform, compatible with the Nitrogen Vacancy (NV) diamond centers on-chip technology, to drastically improve the range of entanglement over 17 free-space wavelengths, or approximatively 12.5 ”m, using mu near-zero metamaterials. We evaluate transient and steady state concurrence demonstrating an order of magnitude enhancement compared to previous works. This is, to the best of our knowledge, the first time that such a long distance is reported using this strategy. Moreover, value of the zero time delay second order correlation function $${g}_{12}^{(2)}(0)$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>12</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> are provided, showing antibunching signature correlated with a high degree of concurrence.