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Physical Review A

Parameter dependence in the atmospheric decoherence of modally entangled photon pairs

Alpha Hamadou Ibrahim, Filippus Stefanus Roux, Thomas Konrad

Published Nov 19, 2014• 31 citations
Publisher

Abstract

When a pair of photons that are entangled in terms of their transverse modes, such as an orbital angular momentum (OAM) basis, propagates through atmospheric turbulence, the scintillation causes a decay of the entanglement. Here, we use numerical simulations to study how this decoherence process depends on the various dimension parameters of the system. The relevant dimension parameters are the propagation distance, the wavelength, the beam radius, and the refractive index structure constant, indicating the strength of the turbulence. We show that beyond the weak scintillation regime, the entanglement evolution cannot be accurately modeled by a single phase screen that is specified by a single dimensionless parameter. Two dimensionless parameters are necessary to describe the OAM entanglement evolution. Furthermore, it is found that higher OAM modes are not more robust in turbulence beyond the weak scintillation regime.

DOI
10.1103/physreva.90.052115

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When a pair of photons that are entangled in terms of their transverse modes, such as an orbital angular momentum (OAM) basis, propagates through atmospheric turbulence, the scintillation causes a decay of the entanglement. Here, we use numerical simulations to study how this decoherence process depends on the various dimension parameters of the system. The relevant dimension parameters are the propagation distance, the wavelength, the beam radius, and the refractive index structure constant, indicating the strength of the turbulence. We show that beyond the weak scintillation regime, the entanglement evolution cannot be accurately modeled by a single phase screen that is specified by a single dimensionless parameter. Two dimensionless parameters are necessary to describe the OAM entanglement evolution. Furthermore, it is found that higher OAM modes are not more robust in turbulence beyond the weak scintillation regime.
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.
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 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.
The decay of OAM entanglement in non-Kolmogorov turbulence has been numerically evaluated. In this work, we explore the evolution of OAM entanglement with higher-order OAM mode in the weak scintillation regime. In particular, the results of the numerical evaluation show that the OAM entanglement state with higher value of the azimuthal mode and larger radial quantum number survives over a longer distance. Meanwhile, the beam parameters and turbulence parameters usually have significant influences on OAM entanglement. In addition, it is demonstrated that the effect of turbulence on the OAM entanglement is the most serious when the generalized exponent is around 3.07.