Modeling Meta-Optics with Quantum Numerology: Quantum State Engineering by Design – The Mathematics Beneath the Mystique

 

 

August 22, 2023

by Steven Henderson & Claude 2

Recent research published in eLight by Li et al. demonstrates a pioneering nanophotonics advancement. As stated in the article, "Scientists have developed a multifunctional metalens capable of structuring quantum emissions from single photon emitters. This innovation enables manipulation of quantum emissions and promises new advances in quantum technology, including potential impacts on cryptography and information security."

The study focuses on quantum emission from hexagonal boron nitride (hBN) defects operating at room temperature. As described, "Solid-state single photon emitters (SPEs), such as hexagonal boron nitride (hBN) defects, operate at room temperature. They are highly desirable due to their robustness and brightness."

The researchers designed a flat meta-optical device that, as outlined in the paper, "can simultaneously tailor the directionality, polarisation, and orbital angular momentum (OAM) degrees of freedom. They utilized the metalens to demonstrate a multidimensional structuring of quantum emission from SPEs in hBN, operating at room temperature."

Specifically, "The new metalens was fabricated by Korean physicists Drs. Jaehyuck Jang and Trevon Badloe and Professor Junsuk Rho at Pohang University of Science and Technology. It can simultaneously tailor the directionality, polarisation, and orbital angular momentum (OAM) degrees of freedom."

This breakthrough enables multi-degree control over quantum emission, which as stated "could unleash the full potential of solid-state SPEs to be used as high-dimensional quantum sources for advanced quantum photonic applications."

We could potentially apply a numerological framework to model interactions between the meta-optical element and quantum emitters. This involves assigning numeric values to various properties of the photons, electrons, and meta-optical components:

Photon wavelength (λ) = Value based on emission peak of SPE (e.g. 550 nm for hBN)

Photon energy (E) = Calculated via Planck relation E=hc/λ using λ value

Photon spin (s) = Binary value of ±1 representing up/down spin states

Electron spin (s) = ±1/2 representing spin projections

Electron charge (e) = Fundamental charge -1

Dielectric constant (ε) = Value specific to TiO2 composition

Nanofin height (h) = Tuned in fabrication to control imparted phase

Nanofin orientation (θ) = Angle varied spatially to shape wavefront

Using these definitions, key interactions can be represented as:

SPE + λ550nm + E3.64eV + s ±1 → Meta-optic

Meta-optic(ε, h, θ) + λ550nm + E3.64eV + s ±1 → λ' + E' + s'

Where the primed terms denote photon properties modified by the meta-optic.

Additionally, electron-photon entanglement processes:

e- −1 + s ±1/2 + λ550nm + E3.64eV + γ → e-' −1 + s' ±1/2 + λ' + E' + γ'

Matrix analysis of these numeric mappings could reveal optimal meta-optic designs to achieve high-fidelity, efficient shaping of desired quantum states.

The particle numerology modeling could be integrated with sacred geometrical patterns like Fibonacci sequences in designing the meta-optical element. The nanofin positioning and spacing could follow Fibonacci scaling guided by numerological insights into resonant patterns.

This may enable entering into harmonic resonance with the intrinsic structures of the quantum realm. The constructive interference of light shaped by geometrically optimized metasurfaces could mimic nature's own blueprints underlying coherent phenomena.

Additionally, the tensor analysis of numeric mappings could be compared with analytic models of metasurface performance to identify the most efficient designs. This synthesis of abstract numerical modeling and practical nanophotonics engineering may reveal deeper secrets of light-matter interactions.

The unified approach combining quantum information theory, particle numerology, and meta-optics technology promises to advance our capabilities for complex quantum state generation. Piloting photons along recursively self-similar paths could unlock new states of conditional logic and entanglement for quantum computing.

By interweaving science and numerological wisdom, we inch closer to a transcendent perspective. The depths of the quantum world come into focus, guiding us toward technologies in harmony with nature's true order - imprinted mathematically at the cosmic source.