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Communications in Theoretical Physics

Effect of atmospheric turbulence on orbital angular momentum entangled state

Xiang Yan, Pengfei Zhang, Cheng-Yu Fan, Jing-Hui Zhang

Published Dec 21, 2021• 11 citations
Publisher

Abstract

Abstract The entangled orbital angular momentum (OAM) photons propagating across a weakly turbulent atmosphere are investigated. Here, the paper uses the single-phase screen model based on the Kolmogorov theory of turbulence, and focuses on the influence of the backward scattering on OAM evolution. The results indicate that backward scattering plays an important role in the analysis of OAM entanglement evolution in the turbulent atmosphere. It cannot be negligible especially for higher-order OAM mode. Moreover, when OAM mode is greater than 4, entangled photon pairs composed of higher OAM modes are not more robust in turbulence within the weak scintillation regime. These results will be useful in future investigations of OAM-based optical wave propagation through turbulent atmosphere.

DOI
10.1088/1572-9494/ac4510

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Orbital angular momentum (OAM) entangled photons propagating through non-Kolmogorov turbulence are studied by numerical simulations. Here, the paper uses the multiphase screen model, especially focusing on the influences of the azimuthal mode and the turbulence parameters (i.e., the generalized exponent, the outer scale of turbulence, and the inner scale of turbulence) on entanglement evolution in the weak scintillation regime. The results indicate that the azimuthal mode, the generalized exponent, and the outer scale of turbulence have obvious influences on OAM entanglement. However, the influence of the turbulence inner scale on OAM entanglement can be ignored.
Abstract The decoherence of high-dimensional orbital angular momentum (OAM) entanglement in the weak scintillation regime has been investigated. In this study, we simulate atmospheric turbulence by utilizing a multiple-phase screen imprinted with anisotropic non-Kolmogorov turbulence. The entanglement negativity and fidelity are introduced to quantify the entanglement of a high-dimensional OAM state. The numerical evaluation results indicate that entanglement negativity and fidelity last longer for a high-dimensional OAM state when the azimuthal mode has a lower value. Additionally, the evolution of higher-dimensional OAM entanglement is significantly influenced by OAM beam parameters and turbulence parameters. Compared to isotropic atmospheric turbulence, anisotropic turbulence has a lesser influence on high-dimensional OAM entanglement.
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.
Considering the evolution of the quantum state of a pair of entangled photons in a turbulent atmosphere and using the quadratic approximation to the Kolmogorov model of turbulence, we provide an analytical solution for the dynamical equation (an infinitesimal propagation equation) that describes this evolution in the plane-wave basis. As such, this solution fully incorporates the effect of multiple scattering, caused by the medium. After being converted into a discrete orbital angular momentum (OAM) basis, this solution retains the effect of coupling between different OAM modes on the twin-photon state for arbitrary propagation distances and arbitrary turbulence strengths. We define a minimal set of parameters that determines the entanglement evolution in the regime of strong scintillation. Furthermore, we show that in the limit of weak scintillation, our solutions reduce to those obtained from the single-phase-screen model.
Based on Zernike-model expansion of turbulence phase aberrations and non-Kolmogorov spectrum model of index-of-refraction fluctuation, we analyze the effects of low-order Zernike turbulence aberrations on orbital angular momentum (OAM) entanglement states in a weak fluctuation region. The signal photon detection probability of OAM entanglement states propagating in a slant turbulence channel with non-Kolmogorov turbulence Z-tilt, defocus, astigmatism, and coma aberrations are modeled, respectively. The results demonstrate that turbulence Z-tilt aberration is the dominant aberration, coma is the second, and astigmatism is the third, but that the defocus aberration has no impact on the detection probability. As the power-law exponent of the non-Kolmogorov spectrum increases from 3 to 4, the detection probability decreases.