Propagation of Two-Photon Zernike States in Atmospheric Turbulence

TL;DR

This paper studies how two-photon Zernike states propagate through atmospheric turbulence, revealing that partial adaptive optics can significantly reduce crosstalk and preserve spatial correlations.

Contribution

It provides an analytical reduction of propagation integrals for Zernike states and demonstrates the effectiveness of partial adaptive optics in turbulence.

Findings

Turbulence induces azimuthal and radial crosstalk in Zernike states.

Partial adaptive optics correcting up to sixth radial order suppresses crosstalk.

Near-ideal spatial correlations can be restored with limited correction.

Abstract

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. By explicitly removing the lowest-order terms from the discrete turbulence sum, we demonstrate that partial adaptive optics correcting only up to the sixth radial order is sufficient to heavily suppress this crosstalk and restore near-ideal spatial correlations.