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Electromagnetic waves

DEGREE OF DEPOLARIZATION OF QUANTIZATION HERMITE-GAUSSIAN BEAM IN A TURBULENT ATMOSPHERE

Licheng Zhang, Yixin Zhang, Yun Zhu

Published Jan 1, 2013• 2 citations
Publisher

Abstract

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 w 0 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.

DOI
10.2528/pier13041708

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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 w 0 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.
Polarization of light has many applications in quantum information processing, including quantum teleportation and dense coding. In this paper, we investigate the polarization fluctuations of Airy beams propagating in a slant turbulent channel under the "few-photon" limit. Using the quantum Stokes parameters and the quantum degree of polarization, we demonstrate that the degree of polarization of Airy beams increases significantly with the large number of the detection photons, and a higher photon-number level can retain the stability of polarization. Numerical simulations show that the longer propagation distance and the stronger turbulence will lead to less oscillatory behaviors and a decrease in the polarization degree of Airy beams, but a bigger exponential truncation factor will cause an increase in the polarization degree of Airy beams. In contrast with Gaussian beams, the degree of polarization of Airy beams is less affected by atmospheric turbulence and propagation distance under the same conditions, which means that Airy beams possess a resilient ability against turbulence-induced perturbations. These results indicate that Airy beams have great potential for applications in long-distance free-space optical communications to improve the performance of a polarization-encoded free-space quantum communication system.
Multiple-degrees-of-freedom free-space communication combining polarization and high-order spatial modes promises high-capacity communication channel. While high-order spatial modes have been widely exploited for dense coding and high-dimensional quantum information processing, the properties of polarization preservation of high-order spatial beams propagating in turbulent atmosphere have not been comprehensively investigated yet. Here we focus on the properties of polarization preservation of partially coherent Hermite-Gaussian beams propagating along different atmospheric turbulence paths. The analytical expressions for the polarization of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence along different paths have been derived. It is shown that the larger the coherence length is, and the larger the beam order m, n are, the less the polarization is changed. We find that the evolution properties of the polarization in slant-down paths through turbulent atmosphere are similar to the case in free space if the condition zenith angle ξ
In order to study the influence of atmospheric turbulence on the polarization state of the free space quantum communication, the relationship between the refractive index and altitude, the refractive index structure constant and the turbulence dimension is deduced based on two different atmospheric refractive index structural constants models. The turbulence intensity factor κ is introduced and the equation of the variation of the quantum polarization degree with turbulence intensity is established. Through the simulation of the turbulent refractive index and the performance of four different polarization states in the low altitude turbulence environment, the results show that the atmospheric turbulence in the near ground will affect the fluctuation of the degree of polarization, and the degree of polarization varies linearly with the change of turbulence intensity. In the case of polarization |H>, the range of polarization |H> varies from 0 to 0.14 with the change of turbulence intensity. The influence of atmospheric turbulence on four different polarization states is different, and the degree of |H> and |V> depolarization is greater in the daytime and back. The depolarization degree of |-> at night is greater. The relationship between the degree of polarization and the change of turbulence intensity is analyzed by mathematical modeling, which is helpful to select the reasonable experimental scheme and compensate the change of polarization state in the aviation quantum Secure communication channel.
Utilizing the quantized Huygens-Fresnel principle, we study the effects of anisotropic non-Kolmogorov turbulence on the average polarizability of quantization Bessel-Gaussian Schell-model (BGSM) photon beams. We find that the average polarizability has a weak dependence on the outer scale. By decreasing the source transverse coherent width, transmission distance and receiver aperture diameter, or increasing wavelength and photon number, we can improve the average polarizability. In addition, the average polarizability increases with increasing inner scale and anisotropic factor, or decreasing refractive-index structure parameter. This work reveals that we can utilize higher number of photons, lower source transverse coherent width and longer “window” wavelength to improve the performance of a polarizationencoded free-space quantum communication system.
Non-classical polarization properties of dark hollow beams propagating through non-Kolmogorov turbulence are studied. The analytic equation for the polarization degree of the quantization partially coherent dark hollow beams is obtained. It is found that the polarization fluctuations of the quantization partially coherent dark hollow beams are dependent on the turbulence factors and beam parameters with the detection photon numbers. Furthermore, an investigation of the changes in the on-axis propagation point and off-axis propagation point shows that the polarization degree of the quantization partially coherent dark hollow beams presents oscillation for a short propagation distance and gradually returns to zero for a sufficiently long distance.
The orbital angular momentum (OAM) state of light can potentially be used to implement higher dimensional entangled systems for quantum communication. Unfortunately, optical fibers in use today support only modes with zero OAM values. Free-space quantum communication is an alternative to traditional way of communicating through optical fibers. However the refractive index fluctuation of the atmosphere gives rise to random phase aberrations on a propagating optical beam. To transmit quantum information successfully through a free-space optical channel, one needs to understand how atmospheric turbulence influences quantum entanglement. Here, we present a numerical study of the evolution of quantum entanglement between a pair of qubits. The qubits consist of photons entangled in the OAM basis. The photons propagate in a turbulent atmosphere modeled by a series of consecutive phase screens based on the Kolmogorov theory of turbulence. Maximally entangled initial states are considered, and the concurrence is used as a measure of entanglement. We show how the evolution of entanglement is influenced by various parameters such as the beam waist, the strength of the turbulence and the wavelength of the beam. We restricted our analysis to the OAM values l = ±1 and we compared our results to previous work.