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  • Open Access

Propagation of two-photon Zernike states in atmospheric turbulence

Hakob Avetisyan*

Vahagn Abgaryan†

  • *Contact author: h.avetisyan@yerphi.am
  • †Contact author: vahagnab@googlemail.com
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Phys. Rev. A 114, 023730 – Published 27 August, 2026

DOI: https://doi.org/10.1103/q6yy-zfyn

Abstract

We analyze propagation and detection of two-photon states expanded in Zernike modes through atmospheric turbulence using the extended Huygens-Fresnel formalism. For spontaneous parametric down-conversion states prepared with a single Zernike pump mode, we analytically reduce the eight-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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References (32)

  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys. Rev. A 45, 8185 (1992).
  2. V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Screw dislocations in light wavefronts, J. Mod. Opt. 39, 985 (1992).
  3. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Astigmatic laser mode converters and transfer of orbital angular momentum, Opt. Commun. 96, 123 (1993).
  4. M. J. Padgett and J. Courtial, Poincaré sphere equivalent for light beams containing orbital angular momentum, Opt. Lett. 24, 430 (1999).
  5. G. S. Agarwal, SU(2) structure of the Poincaré sphere for light beams with orbital angular momentum, J. Opt. Soc. Am. A 16, 2914 (1999).
  6. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Entanglement of the orbital angular momentum states of photons, Nature (London) 412, 313 (2001).
  7. A. Vaziri, G. Weihs, and A. Zeilinger, Experimental two-photon, three-dimensional entanglement for quantum communication, Phys. Rev. Lett. 89, 240401 (2002).
  8. S. Goel, B. Ghosh, and M. Malik, Quantum information processing with spatially structured light, Adv. Photonics 8, 014005 (2025).
  9. S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion, Phys. Rev. A 69, 023811 (2004).
  10. S. P. Walborn, S. Pádua, and C. H. Monken, Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion, Phys. Rev. A 71, 053812 (2005).
  11. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, Bellingham, 2005).
  12. R. W. Boyd, B. Rodenburg, M. Mirhosseini, and S. M. Barnett, Influence of atmospheric turbulence on the propagation of quantum states of light using plane-wave encoding, Opt. Express 19, 18310 (2011).
  13. Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran, M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing, Opt. Lett. 38, 4062 (2013).
  14. M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Communication with spatially modulated light through turbulent air across Vienna, New J. Phys. 16, 113028 (2014).
  15. D. Vasylyev, A. A. Semenov, and W. Vogel, Atmospheric quantum channels with weak and strong turbulence, Phys. Rev. Lett. 117, 090501 (2016).
  16. M. Ghalaii and S. Pirandola, Quantum communications in a moderate-to-strong turbulent atmosphere, Commun. Phys. 5, 38 (2022).
  17. C. Paterson, Atmospheric turbulence and orbital angular momentum of single photons for optical communication, Phys. Rev. Lett. 94, 153901 (2005).
  18. G. A. Tyler and R. W. Boyd, Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum, Opt. Lett. 34, 142 (2009).
  19. H. Avetisyan and C. H. Monken, Higher order correlation beams in atmosphere under strong turbulence conditions, Opt. Express 24, 2318 (2016).
  20. H. Avetisyan and C. H. Monken, Mode analysis of higher-order transverse-mode correlation beams in a turbulent atmosphere, Opt. Lett. 42, 101 (2017).
  21. H. Avetisyan and G. Nikoghosyan, Quantum aberrations: Entangling photons with Zernike polynomials, Phys. Rev. A 112, 043714 (2025).
  22. R. J. Noll, Zernike polynomials and atmospheric turbulence, J. Opt. Soc. Am. 66, 207 (1976).
  23. S. N. Bezdidko, The use of Zernike polynomials in optics, Sov. J. Opt. Technol. 41, 425 (1974).
  24. D. L. Fried, Statistics of a geometric representation of wavefront distortion, J. Opt. Soc. Am. 55, 1427 (1965).
  25. W. J. Tango, The circle polynomials of Zernike and their application in optics, Appl. Phys. 13, 327 (1977).
  26. E. C. Kintner and R. M. Sillitto, A new “analytic” method for computing the optical transfer function, Optica Acta: Int. J. Opt. 23, 607 (1976).
  27. A. J. E. M. Janssen, New analytic results for the Zernike circle polynomials from a basic result in the Nijboer-Zernike diffraction theory, J. Eur. Opt. Soc.-Rapid Publ. 6, 11028 (2011).
  28. E. C. Kintner, Some comments on the use of the Zernike polynomials in optics, Opt. Commun. 18, 235 (1976).
  29. S. Walborn, C. Monken, S. Pádua, and P. Souto Ribeiro, Spatial correlations in parametric down-conversion, Phys. Rep. 495, 87 (2010).
  30. S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Two-photon entanglement of orbital angular momentum states, Phys. Rev. A 65, 033823 (2002).
  31. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
  32. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 8th ed. (Elsevier, New York, 2015).

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Phys. Rev. A 114, 023730– Published 27 August, 2026
  • Received 12 March 2026
  • Accepted 11 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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