[论文解读] Propagation of Two-Photon Zernike States in Atmospheric Turbulence

Hakob Avetisyan, Vahagn Abgaryan|arXiv (Cornell University)|Mar 12, 2026

Adaptive optics and wavefront sensing被引用 0

一句话总结

The paper develops a discrete, algebraic framework to propagate and detect two-photon states expanded in Zernike modes through atmospheric turbulence, showing turbulence-induced crosstalk is dominated by low-order aberrations and can be mitigated with partial adaptive optics.

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.

研究动机与目标

• Motivate the use of Zernike modes as a physically meaningful basis for describing quantum states of light and their robustness to turbulence.
• Develop an extended Huygens–Fresnel formalism in the Zernike basis to model turbulence-induced mode coupling.
• Derive analytical expressions for joint two-photon detection probabilities in turbulence.
• Show how turbulence relaxes azimuthal and radial selection rules and how partial adaptive optics can mitigate crosstalk.
• Provide a framework connecting state preparation, modal structure, and turbulence effects in SPDC-generated photon pairs.

提出的方法

• Represent pupil and field operators in the Zernike basis and use A- and Gamma-coefficients to capture mode coupling and addition rules.
• Incorporate atmospheric turbulence via the extended Huygens–Fresnel principle and ensemble-average the random phase to obtain turbulence-modified joint detection probabilities.
• Derive exact reductions from continuous propagation integrals to a discrete, finite-dimensional tensor framework.
• Apply the framework to SPDC-generated two-photon states with single Zernike-pump modes to obtain analytical expressions for detection amplitudes.
• Analyze no-turbulence limits to recover exact selection rules and then study turbulence-induced crosstalk and its suppression by truncating low-order modes (partial AO).
• Utilize the Fraunhofer regime to relate pupil-plane Zernike expansions to image-plane transforms through Fourier–Zernike identities.

实验结果

研究问题

• RQ1 How does atmospheric turbulence affect the selection rules and mode coupling of two-photon states expressed in the Zernike basis?
• RQ2 Which low-order Zernike modes dominate turbulence-induced crosstalk, and how can partial adaptive optics suppress it?
• RQ3 Can the continuous propagation problem be exactly reduced to a discrete algebraic framework in the Zernike basis, and what are the resulting implications for SPDC entanglement?
• RQ4 What are the differences between no-turbulence and turbulence scenarios in terms of azimuthal and radial conservation laws for two-photon states?
• RQ5 How does the pump mode structure influence the final two-photon detection probabilities under turbulence?

主要发现

• In the absence of turbulence, exact azimuthal conservation and a radial-order bound are enforced by Zernike addition rules.
• Turbulence relaxes these constraints, driving azimuthal and radial crosstalk dominated by low-order aberration modes.
• Removing the lowest-order terms from the turbulence sum significantly suppresses crosstalk and restores near-ideal spatial correlations.
• Partial adaptive optics correcting up to the sixth radial order can heavily suppress turbulence-induced crosstalk at weak-to-moderate turbulence levels.
• Even under stronger turbulence, the dominant correlation peak remains, with residual leakage confined to adjacent modes.