Exciton-polariton mediated interaction between two nitrogen-vacancy color centers in diamond using two-dimensional transition metal dichalcogenides
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2021-02-04 |
| Journal | Physical review. B./Physical review. B |
| Authors | J. C. G. Henriques, Bruno Amorim, N. M. R. Peres |
| Institutions | QuantaLab, University of Minho |
| Citations | 5 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive Summaryā- Enhanced Quantum Interaction: The study demonstrates a strong, tunable quantum interaction between two negatively charged Nitrogen-Vacancy (NV-) color centers in diamond.
- Polariton Mediation: This interaction is mediated by Exciton-Polaritons (EPs) propagating in a proximal monolayer of a Transition Metal Dichalcogenide (TMD), such as WS2.
- Long-Range Coupling: Due to the 2D nature of the polaritons, the NV- coupling (gij) and decay rates (Vij) exhibit a long-range spatial decay proportional to Ļ-1/2, which significantly dominates the standard electrostatic dipole-dipole interaction (Ļ-3) at distances up to 100 nm.
- Superradiance Prediction: The model predicts the occurrence of Exciton-Polariton mediated Superradiance (Ī > 1) and Subradiance, which are highly sensitive to the NV- separation (Ļ) and the orientation of their electric dipole moments.
- Tunability: Interaction parameters and energy level renormalizations (Lamb shifts Īi) are extremely sensitive to the distance between the NV- centers and the TMD layer.
- General Applicability: The derived quantum master equation framework is applicable to other solid-state emitters, including color centers in hexagonal boron nitride (hBN), facilitating the design of all-van der Waals quantum devices.
Technical Specifications
Section titled āTechnical Specificationsā| Parameter | Value | Unit | Context |
|---|---|---|---|
| NV- Optical Transition Energy (ħĻ0) | 1.945 | eV | Energy difference between the NV- two-levels. |
| NV- Electric Dipole Moment (Āµ) | 1.5 | D | Magnitude used for both dipoles in the optical transition. |
| TMD Exciton Energy (ħĻex) | 1.94 | eV | Typical A-exciton energy (WS2 parameters used). |
| Exciton Oscillator Strength (fex) | 0.39 | dimensionless | Describes exciton coupling to the electric field. |
| Exciton Non-Radiative Decay Rate (Ī³nr) | 1.99 | meV | Loss rate for the exciton component. |
| Exciton Dephasing Rate (Ī³d) | 0.04 | meV | Exciton dephasing rate. |
| TMD Effective Thickness (d) | 0.65 | nm | Thickness of the monolayer TMD. |
| NV- Energy Renormalization (Īi) | ~25 | ĀµeV | Calculated Lamb shift magnitude. |
| Polariton Wavelength (Ī»p) | ~37 | nm | Polariton wavelength at the NV- transition energy (ħĻ0). |
| Interaction Decay Profile (gij, Vij) | Ļ-1/2 | N/A | Spatial decay rate of exciton-polariton mediated coupling (Ļ is in-plane separation). |
| Interaction Dominance Range | Ļ > Ī»p/10 | N/A | Range where polariton interaction dominates over Ļ-3 dipole-dipole interaction. |
| Superradiance Condition (Ī) | > 1 | N/A | Figure of merit indicating coherent emission enhancement. |
| Operating Temperature | Low | K | Parameters (Table I) derived for T = 4 K (WS2). |
Key Methodologies
Section titled āKey Methodologiesā- System Configuration: Modeled two NV- centers (two-level systems) embedded in a diamond slab (dielectric constant Īµ1) positioned at distances z1 and z2 above a TMD monolayer (at z=0). The TMD rests on a second dielectric (Īµ2, taken as vacuum).
- Hamiltonian Formulation: The system dynamics are described by a modified Dicke Hamiltonian, including terms for the NV- centers (HNV), the TMD exciton-polaritons (Hex-p) modeled as independent bosons, and the dipole coupling interaction (Hint).
- TMD Optical Modeling: The TMD optical response is characterized by its frequency-dependent susceptibility Ļ(Ļ), which incorporates the exciton resonance (Ļex) and intrinsic decay rates (Ī³nr, Ī³d). This susceptibility determines the optical conductivity Ļ(Ļ).
- Polariton Dispersion Relation: The exciton-polariton energy dispersion (Ļq) is solved implicitly using the boundary conditions for the electric field at the TMD interface, requiring the real part of the susceptibility to be negative. An approximate analytical solution (Eq. 13) is used for large momenta (q).
- Quantum Master Equation Derivation: The dynamics of the NV- centersā reduced density matrix Ļ(t) are governed by the Lindblad equation, derived by tracing out the exciton-polariton degrees of freedom under the Born-Markov and rotating wave approximations.
- Greenās Function Formalism: The resulting effective parametersāLamb shifts (Īi), collective decay rates (Vij), and coupling constants (gij)āare calculated explicitly using the exciton-polariton Greenās functions (retarded/advanced) and the electric field spectral function (AĪ±Ī²).
- Polariton-Pole Approximation: The exciton-polariton Greenās function is used as a polariton-pole approximation to the full electromagnetic Greenās function, valid when the NV- frequency is close to the polariton frequency and the centers are near the TMD.
Commercial Applications
Section titled āCommercial Applicationsā- Scalable Quantum Computing: The strong, long-range (Ļ-1/2) polariton-mediated coupling provides a robust mechanism for implementing two-qubit gates and building scalable quantum registers using distant solid-state NV- qubits.
- Quantum Nanophotonics and Light Sources: Control over collective emission phenomena (Superradiance and Subradiance) allows for the engineering of highly efficient, directional, and fast light emitters or quantum memories integrated into chip-scale devices.
- Integrated Quantum Devices: The methodology supports the development of quantum optics devices built entirely from van der Waals heterostructures (e.g., hBN emitters coupled via TMDs), offering high integration density and material compatibility.
- Tunable Quantum Sensors: The extreme sensitivity of the NV- energy shifts and decay rates to the distance and dielectric environment suggests applications in highly localized, tunable quantum sensing and microscopy of 2D materials and interfaces.
- Solid-State Quantum Networks: The enhanced long-range interaction is critical for linking quantum nodes across a chip, forming the basis for solid-state quantum communication networks.
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.
Tech Support
Section titled āTech SupportāOriginal Source
Section titled āOriginal SourceāReferences
Section titled āReferencesā- 2017 - Quantum Optics and Nanophotonics