Propagation of Higher Order Correlation Beams in Turbulent Atmosphere

Abstract

This Thesis deals with theoretical aspects of atmospheric propagationof correlation beams. The correlation beam is prepared in the processof low gain spontaneous parametric down-conversion in the two photonregime within the thin crystal approximation with the correlateddirect detection scheme. The joint detection probability amplitudehas a beam-like behavior of spatial correlations in two-photon states,hence the name. The correlation beam is the most practical tool invarious quantum communication protocols, thus, studying its propagationin the atmosphere is of practical and fundamental interest opening a possibility of performing a global quantum communication. Moreover, one can prepare two-qudit states to implement a communication with large alphabets. To this end, we analytically calculated the atmospheric two-photon joint detection probability when the pump represents a coherent Hermite- or Laguerre Gaussian mode of any order as well as a partially coherent beam from a Gaussian- Schell model source. As an important side result, we showed that the joint probability for the latter case is a convex combination of the former ones. Our results show that the expressions for fourth-order correlation functions are similar to those of intensities of classical beams: a manifestation of the concept of the correlation beam. Additionally, we showed that with the strength of the turbulence the amount of the HG00 mode is appreciable even in moderate turbulence, meaning that the cross-talk between modes increases with turbulence degrading the dimensionality of the alphabet based on higher-order Gaussian modes. To quantify the crosstalk between different modes, which is inevitable when propagating in the atmosphere, we made a mode analysis of the correlation beam. An operational procedure to implement projective measurements on two-photon multimode states is also given. Because of the mathematical difficulty, we considered only the zeroth order Gaussian pump. We calculated the probability of single photodetections and comparedwith the two-photon joint detection probability. The former probability degrades rapidly after short distances of propagation, whereasthe latter one is considerable even after five or more kilometers ofpropagation. The analytical approach used in this Thesis enables oneto deal with the subject more deeply. Finally, we set up two approached to solve certain problems. One of them concerns the correction of the corrupted two-photon wave phase using Zernike polynomials. The other the inference of atmospheric parameters by measuring the correlation beam. Certainly, the parameters that can be inferred only with fourth order statistics, e.g., the scintillation index, the intensity correlation width, are easier toinfer using a correlation beam, which is a fourth-order phenomenon.