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Exciton-polariton mediated interaction between two nitrogen-vacancy color centers in diamond using two-dimensional transition metal dichalcogenides

MetadataDetails
Publication Date2021-02-04
JournalPhysical review. B./Physical review. B
AuthorsJ. C. G. Henriques, Bruno Amorim, N. M. R. Peres
InstitutionsInternational Iberian Nanotechnology Laboratory, University of Minho
Citations5
AnalysisFull AI Review Included

Technical Documentation & Analysis: Exciton-Polariton Mediated NV Center Interaction

Section titled “Technical Documentation & Analysis: Exciton-Polariton Mediated NV Center Interaction”

This documentation analyzes the theoretical framework for achieving strong, tunable interactions between negatively charged Nitrogen-Vacancy (NV-) centers in diamond, mediated by exciton-polaritons supported by a two-dimensional (2D) Transition Metal Dichalcogenide (TMD) monolayer. This research is critical for advancing solid-state quantum computation and nanophotonics.

  • Core Application: Demonstrates the feasibility of exciton-polariton mediated superradiance and subradiance in coupled NV- centers, essential for scalable quantum computing architectures.
  • Critical Material Requirement: Requires ultra-high purity, single-crystal diamond (SCD) substrates capable of hosting precisely positioned NV centers in close proximity (2-4 nm) to the TMD layer.
  • Interaction Mechanism: The interaction parameters (coupling $g_{ij}$ and decay rates $\gamma_{ij}$) are highly sensitive to the NV center’s distance ($z$) from the TMD and the relative orientation of the electric dipole moment ($\mu$).
  • Decay Characteristics: The 2D nature of the exciton-polaritons causes the interaction parameters to decay spatially as $\rho^{-1/2}$ (where $\rho$ is the in-plane separation), significantly extending the interaction range compared to conventional electrostatic dipole-dipole interaction ($\rho^{-3}$).
  • Observed Phenomena: Theoretical predictions show superradiance ($\Gamma > 1$) and subradiance ($\Gamma < 1$) can be observed for NV centers separated by up to 100 nm.
  • 6CCVD Value Proposition: 6CCVD provides the necessary high-purity SCD material with industry-leading surface quality (Ra < 1 nm) and precise thickness control (down to 0.1 ”m) required for successful TMD integration and nanoscale device fabrication.

The following hard parameters were extracted from the theoretical model (Table I and text) used to simulate the NV-TMD system dynamics.

ParameterValueUnitContext
NV Center Optical Transition ($\hbar\omega_0$)1.945eVEnergy difference between NV levels.
Electric Dipole Moment ($\mu$)1.5DMagnitude of the dipole moment for the optical transition.
A-Exciton Energy ($\hbar\omega_{ex}$)1.94eVTypical energy for A-exciton in TMD (e.g., WS2).
Exciton Oscillator Strength ($f_{ex}$)0.39-Describes exciton coupling to the electric field.
Non-Radiative Decay Rate ($\gamma_{nr}$)1.99meVLoss rate for excitons (device dependent).
Dephasing Rate ($\gamma_d$)0.04meVDephasing rate for excitons (device dependent).
TMD Effective Thickness ($d$)0.65nmThickness of the monolayer TMD.
Background Susceptibility ($\chi_{bg}$)15-Background contribution to susceptibility.
NV-TMD Separation ($z$)2, 3, 4nmCritical distances analyzed for parameter sensitivity.
Polariton Wavelength ($\lambda_p$)$\approx 37$nmPolariton wavelength at the NV transition energy ($\hbar\omega_0$).
Superradiance Range ($\rho$)Up to 100nmMaximum separation for observable super/subradiance.

The research employed a rigorous quantum optics approach to model the coupled NV-center/TMD system.

  1. System Modeling: NV centers are modeled as two-level artificial atoms embedded in a diamond dielectric ($\epsilon_1$). The TMD monolayer is positioned at $z=0$, backed by a vacuum dielectric ($\epsilon_2$).
  2. Hamiltonian Formulation: The system is described using a modified Dicke model Hamiltonian ($H = H_{NV} + H_{ex-p} + H_{int}$), coupling the NV two-level systems to the multimode exciton-polariton boson field.
  3. TMD Optical Properties: The exciton-polariton dispersion relation is derived from the TMD’s optical conductivity ($\sigma(\omega)$), which is related to its susceptibility ($\chi(\omega)$). Exciton-polaritons exist only where the real part of $\chi(\omega)$ is negative (1.940 eV to 1.965 eV).
  4. Quantum Dynamics (Lindblad Equation): The dynamics of the NV centers are governed by the optical Lindblad equation, derived by tracing out the exciton-polariton degrees of freedom (the “bath”).
  5. Green’s Function Analysis: All critical parameters—Lamb shift ($\Delta_i$), coupling ($g_{ij}$), and decay rates ($\gamma_{ij}$)—are expressed analytically in terms of the exciton-polariton Green’s functions.
  6. Approximation: Calculations utilize the polariton-pole approximation to the Green’s function, valid when the NV-center frequency is close to the exciton-polariton frequency and the NV centers are in close proximity to the TMD.

This research relies fundamentally on the availability of high-quality diamond materials with exceptional surface characteristics and precise control over defect placement. 6CCVD is uniquely positioned to supply the foundational materials necessary to replicate and extend this quantum research.

To successfully host and couple NV centers to a 2D TMD layer, the following 6CCVD materials are required:

Research Requirement6CCVD Material SolutionKey Capability Match
High-Purity Host CrystalOptical Grade Single Crystal Diamond (SCD)Essential for minimizing background defects and ensuring long coherence times for NV centers.
Thin Layer IntegrationSCD Wafers (0.1 ”m to 500 ”m)Provides the necessary thin diamond layer for NV centers to be positioned within 2-4 nm of the TMD surface.
Precise Surface InterfaceSCD Polishing (Ra < 1 nm)Achieving nanoscale proximity (2-4 nm) to the TMD requires atomic-scale surface flatness, a core 6CCVD capability.
Potential for Gating/ContactsBoron-Doped Diamond (BDD) or MetalizationIf external gates are required for charge control (as mentioned in the introduction), 6CCVD offers BDD substrates or custom metalization services.

The success of this experiment hinges on precise material engineering, which is a specialty of 6CCVD:

  • Custom Dimensions: 6CCVD can supply SCD plates and wafers up to 125 mm (PCD) or custom dimensions suitable for integration into complex nanophotonic setups.
  • Ultra-Precise Polishing: We guarantee surface roughness (Ra) < 1 nm on SCD, ensuring the critical nanoscale separation ($z$) between the NV center and the TMD layer is maintained uniformly across the device area.
  • Metalization Services: For researchers extending this work to include electrical control or readout, 6CCVD offers in-house deposition of standard metals (Au, Pt, Pd, Ti, W, Cu) for custom contact geometries.
  • Substrate Thickness: We provide substrates up to 10 mm thick for robust handling, while maintaining active SCD layers as thin as 0.1 ”m for optimal quantum interaction.

The theoretical findings emphasize the extreme sensitivity of interaction parameters to dipole orientation and separation. 6CCVD’s in-house PhD team specializes in the material science of MPCVD diamond and its application in quantum systems.

  • Material Selection Consultation: Our experts can assist researchers in selecting the optimal SCD grade, thickness, and surface preparation method to maximize NV center quality and minimize surface defects that could interfere with TMD deposition.
  • Integration Guidance: We provide technical support regarding the integration of diamond materials with 2D heterostructures for similar Quantum Nanophotonics and Solid-State Qubit projects.
  • Global Logistics: We ensure reliable global shipping (DDU default, DDP available) for sensitive materials required for cutting-edge research.

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

View Original Abstract

In this paper, starting from a quantum master equation, we discuss the interaction between two negatively charged nitrogen-vacancy color centers in diamond via exciton-polaritons propagating in a two-dimensional transition metal dichalcogenide layer in close proximity to a diamond crystal. We focus on the optical 1.945 eV transition and model the nitrogen-vacancy color centers as two-level (artificial) atoms. We find that the interaction parameters and the energy-level renormalization constants are extremely sensitive to the distance of the nitrogen-vacancy centers to the transition-metal dichalcogenide layer. Analytical expressions are obtained for the spectrum of the exciton-polaritons and for the damping constants entering the Lindblad equation. The conditions for occurrence of exciton mediated superradiance are discussed.

  1. 2017 - Quantum Optics and Nanophotonics