Hakob Avetisyan | Searcharxiv

arXiv2026

Propagation of Two-Photon Zernike States in Atmospheric Turbulence

We analyze propagation and detection of two-photon states expanded in Zernike modes through atmospheric turbulence using the extended Huygens-Fresnel formalism. For SPDC states prepared with a single Zernike pump mode, we analytically reduce the 8-dimensional continuous propagation integrals to an exact, discrete modal expansion. In the absence of turbulence, Zernike addition enforces conservation of azimuthal index and a strict radial-order bound. Turbulence relaxes these constraints, driving structured azimuthal and radial crosstalk dominated by low-order aberration modes.

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arXiv2025

Quantum Aberrations: Entangling Photons with Zernike Polynomials

We introduce Zernike polynomials as a novel degree of freedom for encoding quantum information in the spatial structure of photons. Building on their orthogonality and completeness over the unit disc, we develop a framework for generating, manipulating, and detecting photons in Zernike modes, and propose methods for realizing single-photon and two-photon Zernike wave packets. We demonstrate analytically that two-photon states generated via spontaneous parametric down- conversion exhibit mode entanglement in the Zernike basis, with correlations arising from selection rules enforced by Clebsch-Gordan coefficients. Our results open a new pathway for structured spatial entanglement, complementary to schemes based on Laguerre-Gaussian or Hermite-Gaussian modes, and suggest practical experimental implementations based on holographic modulation and optical Fourier techniques.

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