Based on quantum Stokes operators and non-Kolmogorov spectrum model of index-of-refraction fluctuation, the analytical formulas for the quantum degree of depolarization of quantization Hermite-Gaussian (QHG) beams propagating in a turbulent atmosphere slant channel are derived. The nonclassical polarization properties of QHG beams propagating in turbulent atmosphere are studied numerically. It is found that the polarization fluctuations of QHG beams are dependent of the turbulence factors such as spectrum powerlaw exponent, refractive index structure parameter at the ground and zenith angle. The degree of depolarization of QHG beams has a saltation and reaches the minimum value at spectrum power-law exponent α = 11/3, the refractive index structure parameter at the ground of the turbulent atmosphere slightly affects the polarization degree of QHG beams which have travelled a long distance, and the change of polarization degree decreases with the increasing zenith angle. Furthermore, the numerical simulations show that QHG beams with higher photonnumber level, lower beam order, shorter wavelength are less affected by the turbulence. These results indicate that One can choose low-order QHG beams with wavelength λ = 690 nm as optical carrier, increase photon number, set the size of transmitting aperture ω0 as about 0.1 m, and detect communication signals at the central region of beams to improve the performance of a polarization-encoded free-space quantum communication system.
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