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arXiv:1903.04539 · Journal of Physics A Mathematical and Theoretical

Universal entanglement decay of photonic orbital angular momentum qubit states in atmospheric turbulence: an analytical treatment

David Bachmann, Vyacheslav Shatokhin, Andreas Buchleitner

Published Aug 30, 2019• 12 citations
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Abstract

Abstract We study the entanglement evolution of photonic orbital angular momentum qubit states with opposite azimuthal indices l 0 , in a weakly turbulent atmosphere. Using asymptotic methods, we deduce analytical expressions for the amplitude of turbulence-induced crosstalk between the modes l 0 and − l 0 . Furthermore, we analytically establish distinct, universal entanglement decay laws for Kolmogorov’s turbulence model and for two approximations thereof.

DOI
10.1088/1751-8121/ab3f3c

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•Sep 16, 2017•0 citations
Abstract We study the entanglement evolution of photonic orbital angular momentum qubit states with opposite azimuthal indices l 0 , in a weakly turbulent atmosphere. Using asymptotic methods, we deduce analytical expressions for the amplitude of turbulence-induced crosstalk between the modes l 0 and − l 0 . Furthermore, we analytically establish distinct, universal entanglement decay laws for Kolmogorov’s turbulence model and for two approximations thereof.
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.
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.
We consider the non-horizontal distributions of orbital angular momentum biphotons through free-space atmospheric channels, in which case the non-Kolmogorov turbulent effects shall be considered. By considering the case of initial non-perfect resource, i.e., the orbital angular momentum biphotons are initially prepared in an extended Werner-like state, we investigate the non-Kolmogorov effects on the propagations of nonclassical correlations, including quantum entanglement and quantum discord. It is found that universal decay laws of entanglement and discord also exist for non-Kolmogorov turbulence but with their decay curves different from that of entanglement for Kolmogorov turbulence reported by Leonhard et al. [Phys. Rev. A91, 012345 (2015)PLRAAN1050-294710.1103/PhysRevA.91.012345]. We show that the universal decay laws are dependent on the power-law exponent of the non-Kolmogorov spectrum and compare the differences of decay properties between entanglement and discord caused by non-Kolmogorov turbulence.
We investigate the decay properties of the quantum coherence and nonclassical correlations of 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 entanglement when the initial state of two photons is not maximally entangled. We 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.