The NV metamaterial - Tunable quantum hyperbolic metamaterial using nitrogen vacancy centers in diamond

At a Glance

Metadata	Details
Publication Date	2021-07-21
Journal	Physical review. B./Physical review. B
Authors	Qing Ai, Fuli Li, Wei Qin, Jie-Xing Zhao, C. P. Sun
Institutions	Xi’an Jiaotong University, Beijing Normal University
Citations	26
Analysis	Full AI Review Included

Executive Summary

Core Innovation: Proposal for a novel quantum hyperbolic metamaterial (HMM) realized by embedding Nitrogen-Vacancy (NV) centers within a diamond host lattice.
Mechanism: The ³A₂ -> ³E electronic transition of the NV centers provides a negative electric response in one principal direction, resulting in an indefinite permittivity tensor (ε_xε_z < 0) and hyperbolic dispersion.
Dynamic Tunability: The frequency window for negative refraction is dynamically tunable across a wide range (GHz domain) by varying the applied external magnetic field (B), which shifts the energy spectra of the NV centers.
Fabrication Solution: This NV-metamaterial approach overcomes the significant difficulty of fabricating classical sub-micron elements required for optical-frequency HMMs, utilizing standard diamond synthesis (CVD, ion implantation).
Critical Density: Negative refraction is theoretically feasible at low NV densities, requiring a minimum concentration of 5.00 ppb, which is well within current experimental fabrication capabilities (e.g., 16 ppm).
Engineering Value: The material enables applications including subwavelength imaging (superlens), enhanced spontaneous emission, and control over heat transport and acoustics.

Technical Specifications

Parameter	Value	Unit	Context
Ground State Zero-Field Splitting (D_gs)	2.88	GHz	Electronic ground state (³A₂)
Excited State Zero-Field Splitting (D_es)	1.42	GHz	Electronic excited state (³E)
Strain-Related Coupling (ξ)	70	MHz	Excited state Hamiltonian
Excited State Lifetime (γ^-1)	10	ns	Homogeneous lifetime
Transition Dipole Moment (d)	11	D	Estimated for ³A₂ -> ³E transition
Relative Permittivity (Diamond, ε_D)	5.7	N/A	Pure diamond background
Critical NV Density (n_c)	1.77 x 10²¹	m^-3	Required for one permittivity component (ε⁽¹⁾) to equal 0
Minimum NV Density (n_min)	5.00	ppb	Required to demonstrate negative refraction
Negative Refraction Window (B=0 G, n₀=0.5 ppm)	(-1.46, 2.37)	GHz	Frequency range (Δω)
Negative Refraction Window (B=0 G, n₀=16 ppm)	Significantly broadened	N/A	Increased density broadens the window
NV Center Orientation Angle (α)	109°28’	Degrees	Angle between any pair of the four possible orientations

Key Methodologies

The realization of the NV-metamaterial is based on detailed quantum mechanical and electromagnetic modeling:

NV Center Hamiltonian Definition: The electronic ground state (³A₂) and excited state (³E) Hamiltonians were established, incorporating zero-field splitting (D), magnetic field (B), and strain (ξ) effects.
Optical Transition Selection Rules: Selection rules for the electric dipole-induced optical transition (³A₂ -> ³E) were derived, ensuring conservation of spin and total angular momentum.
Polarization Density Calculation: Linear response theory (Kubo formalism) was used to calculate the polarization density (P) induced by the incident electromagnetic field, dependent on the transition frequencies and NV density (n₀).
Permittivity Tensor Derivation: The relative permittivity tensor (ε_r) was derived, showing that the ³A₂ -> ³E transition causes one principal component (ε_x) to become negative near resonance, while others (ε_z) remain positive.
Local Field Correction: The Lorentz local field theory was applied to account for dipole-dipole interactions, confirming that the local field effects do not qualitatively change the center or width of the negative refraction domain.
Hyperbolic Dispersion Confirmation: The condition ε_xε_z < 0 was established, confirming the material exhibits hyperbolic (indefinite) dispersion, a prerequisite for negative refraction.
Negative Refraction Proof: Maxwell’s equations were solved for a Transverse Magnetic (TH) incident mode at the interface, analytically proving that negative refraction occurs when the Poynting vector component (S_tx) is negative.

Commercial Applications

This technology interlinks quantum devices (NV centers) and metamaterials, enabling advanced functionalities in several high-impact fields:

Subwavelength Optics & Imaging:
- Construction of Superlenses capable of imaging objects far below the classical diffraction limit.
- Subwavelength imaging and focusing applications.
Quantum Emitter Control:
- Spontaneous Emission Enhancement (Purcell effect) by engineering the local electromagnetic environment.
- Lifetime Engineering for quantum emitters, controlling radiative decay rates.
Quantum Sensing:
- NV centers are highly sensitive quantum sensors; the metamaterial structure could enhance sensitivity to external signals (electric field, magnetic field, temperature).
Energy and Transport:
- Advanced control over Heat Transport (thermal metamaterials).
Acoustic Engineering:
- Potential application in Acoustic Metamaterials for magnifying or controlling sound waves (analogous to the electromagnetic hyperlens).
Fundamental Physics Simulation:
- Used in Analogue Cosmology to simulate complex physical phenomena, such as metric signature transitions.

View Original Abstract

We show that nitrogen-vacancy (NV) centers in diamond can produce a novel\nquantum hyperbolic metamaterial. We demonstrate that a hyperbolic dispersion\nrelation in diamond with NV centers can be engineered and dynamically tuned by\napplying a magnetic field. This quantum hyperbolic metamaterial with a tunable\nwindow for the negative refraction allows for the construction of a superlens\nbeyond the diffraction limit. In addition to subwavelength imaging, this\nNV-metamaterial can be used in spontaneous emission enhancement, heat transport\nand acoustics, analogue cosmology, and lifetime engineering. Therefore, our\nproposal interlinks the two hotspot fields, i.e., NV centers and metamaterials.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.104.014109