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arXiv:1408.3324 · Physical Review A

Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence

Nina Leonhard, Vyacheslav Shatokhin, Andreas Buchleitner

Published Jan 30, 2015• 78 citations
arXivHTMLPDF

Abstract

We consider the propagation of two photonic qubits, initially maximally entangled in their orbital angular momenta (OAM), across a weakly turbulent atmosphere. By introducing the phase correlation length of an OAM beam, we show that the photonic entanglement exhibits a universal exponential decay.
DOI
10.1103/physreva.91.012345

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We investigate the decay properties of the quantumness including quantum entanglement, quantum discord, and quantum coherence for two photonic qubits, which are partially entangled in their orbital angular momenta, through Kolmogorov turbulent atmosphere. It is found that the decay of quantum coherence and quantum discord may be qualitatively different from that of quantum entanglement when the initial state of two photons is not maximally entangled. We also derive two universal decay laws for quantum coherence and quantum discord, respectively, and show that the decay of quantum coherence is more robust than nonclassical correlations.
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In this study, we introduce the phase correlation arc of an orbital angular momentum (OAM) beam to investigate the evolution of OAM entanglement. We reveal that the entanglement decay of all OAM states of Laguerre-Gaussian modes in atmospheric turbulence is universal via both numerical predictions and experimental data. A similar evolution law is also theoretically confirmed to exist in Bessel-Gaussian modes. Finally, by using the phase correlation arc, the precise formula of the decay distance dependence on the OAM number is derived, and it exhibits excellent agreement with previous experimental conclusions.
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.
The turbulence-induced decay of orbital-angular-momentum (OAM) entanglement between two photons is investigated numerically and experimentally. To compare our results with previous work, we simulate the turbulent atmosphere with a single phase screen based on the Kolmogorov theory of turbulence. We consider two different scenarios: in the first only one of the two photons propagates through turbulence, and in the second both photons propagate through uncorrelated turbulence. Comparing the entanglement evolution for different OAM values, we found the entanglement to be more robust in turbulence for higher OAM values. We derive an empirical formula for the distance scale at which entanglement decays in terms of the scale parameters and the OAM value.