In this paper, we investigate the propagation of two-mode spatially Gaussian-entangled quantum light fields passing through the turbulence atmosphere. From the propagation formula of the two-mode wave function in the position representation, we have derived the analytical expressions for the fidelity, purity and logarithmic negativity (entanglement) of the resulting quantum state after the long-distance atmospheric transportation. Based on the derived formulae, the effects of the atmospheric turbulences on the evolutions of quantum properties of the resulting two-mode quantum state are discussed in detail under different input parameters of the initial two-mode quantum state. The results show that the maximal distributing distance of quantum entanglement is strongly dependent on the atmospheric conditions: when the atmospheric turbulence becomes stronger and stronger, the maximal distance becomes shorter and shorter, and both the fidelity and purity decrease quicker and quicker as functions of propagating distances. Under a certain atmospheric condition, with the increasing of the input entanglement of the initial two-mode spatially Gaussian-entangled quantum state, the maximal distributing distance for preserving the entanglement gradually increases and always has a saturated (upper) limitation, and both the evolutions of the fidelity and purity are affected by the input parameters of the initial two-mode quantum state, Finally the optimal parameters of the input two-mode quantum state with the fixed input entanglement are discussed in order to obtain the optimal transfer distribution of the quantum entanglement over a long distance under a certain atmosphere. Our theoretical results are very helpful for building the distribution of the quantum entanglement via free-space atmosphere link.
An Optimal Polarization-Entanglement Source: Frequency-Converted SPDC with Degeneracy, Indistinguishability, and Ultra-High Purity Configurable Over a Large Spectral Range
Quadratic Quantum Polarimetry with Entangled Photon Pairs
ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Department of Electronic Materials Engineering, Research School of Physics, The Australian National University（澳大利亚国立大学）；Institute of Applied Physics, Abbe Center of Photonics, Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学应用物理研究所）；Opto-Electronics and Measurement Techniques, Advanced Electronics Centre, Faculty of Information Technology and Electrical Engineering, University of Oulu（奥卢大学信息技术与电气工程学院高级电子中心光电子与测量技术部门）；Institute of Quantum Precision Measurement, State Key Laboratory of Radio Frequency Heterogeneous Integration, College of Physics and Optoelectronic Engineering, Shenzhen University（深圳大学物理与光电工程学院量子精密测量研究所）；Aston Institute of Photonic Technologies, Aston University（阿斯顿大学光子技术研究所）
