Higher order correlation beams in atmosphere under strong turbulence conditions.

Higher order correlation beams, that is, two-photon beams obtained from the process of spontaneous parametric down-conversion pumped by Hermite-Gauss or Laguerre-Gauss beams of any order, can be used to encode information in many modes, opening the possibility of quantum communication with large alphabets. In this paper we calculate, analytically, the fourth-order correlation function for the Hermite-Gauss and Laguerre-Gauss coherent and partially coherent correlation beams propagating through a strong turbulent medium. We show that fourth-order correlation functions for correlation beams have, under certain conditions, expressions similar to those of intensities of classical beams and are degraded by turbulence in a similar way as the classical beams. Our results can be useful in establishing limits for the use of two-photon beams in quantum communications with larger alphabets under atmospheric turbulence.