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Physical Review A

Effects of atmospheric turbulence on the entanglement of spatial two-qubit states

Anand K. Jha, Glenn A. Tyler, Robert W. Boyd

Published May 18, 2010• 49 citations
Publisher

Abstract

We study the effects of atmospheric turbulence on the entanglement of spatial two-qubit states that are prepared using the signal and idler photons produced by parametric down-conversion. Such states are the basic ingredients of quantum information protocols and can be prepared, for example, by making down-converted photons pass through a pair of double-apertures. We make use of the Kolmogorov model for atmospheric turbulence and quantify the entanglement of the two-qubit state in terms of Wootters's concurrence. We restrict our analysis to the two-qubit states that can be represented by density matrices having only two nonzero diagonal elements.

DOI
10.1103/physreva.81.053832

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We study the effects of atmospheric turbulence on the entanglement of spatial two-qubit states that are prepared using the signal and idler photons produced by parametric down-conversion. Such states are the basic ingredients of quantum information protocols and can be prepared, for example, by making down-converted photons pass through a pair of double-apertures. We make use of the Kolmogorov model for atmospheric turbulence and quantify the entanglement of the two-qubit state in terms of Wootters's concurrence. We restrict our analysis to the two-qubit states that can be represented by density matrices having only two nonzero diagonal elements.
The evolution of high-dimensional entanglement in atmospheric turbulence is investigated. We study the effects of turbulence on photonic states generated by spontaneous parametric down-conversion, both theoretically and experimentally. One of the photons propagates through turbulence, while the other is left undisturbed. The atmospheric turbulence is simulated by a single phase screen based on the Kolmogorov theory of turbulence. The output after turbulence is projected into a three-dimensional (qutrit) basis composed of specific Laguerre-Gaussian modes. Full state tomography is performed to determine the density matrix for each output quantum state. These density matrices are used to determine the amount of entanglement, quantified in terms of the negativity, as a function of the scintillation strength. Theoretically, the entanglement is calculated using a single phase screen approximation. We obtain good agreement between theory and experiment.
Quantum entanglement is an essential element for building the backbone of quantum information systems. Our particular interest lies in long-range distribution of entangled photons to facilitate secure data transfer in free space. To achieve this, we rely on photon pairs generated in such a way that their polarization characteristics represent the corresponding qubit states and have a high degree of correlation in measurements. The main focus of this paper is integrity of the quantum states in free-space channels. When transmitted in atmosphere, classical signals suffer from wave front distortions caused by the spatial and temporal fields of the refractive index. However, this mechanism does not have the same bearing on qubit values and their correlation. We study the effects of turbulence on quantum states by utilizing a laboratory testbed that includes an atmospheric chamber developed by the AFRL. It uses a system of controlled components capable of creating various turbulence conditions. When polarized signals are passed through the atmospheric chamber, we analyze the corresponding quantum states and evaluate the degree of entanglement using our mathematical models and existing metrics.
We analyse the effect of atmospheric Kolmogorov turbulence on entangled orbital angular momentum states generated by parametric down-conversion. We calculate joint and signal photon detection probabilities and obtain numerically their dependence on the mode-width-to-Fried-parameter ratio. We demonstrate that entangled photons are less robust to the effects of Kolmogorov turbulence compared to single photons. In contrast, signal photons are more robust than single photons in the lowest-order mode. We also obtain numerically a scaling relation between the value of the mode-width-to-Fried-parameter ratio for which the joint detection probability is a maximum and the momentum mismatch between signal and idler photons after propagation through the medium.
The effect of a decoherence channel, such as a turbulent atmosphere, on the second-order quantum interference in the Hong-Ou-Mandel (HOM) effect is investigated. The investigation includes both theoretical analyses and an experimental implementation of the process. In our experiment, entangled input states are prepared with spontaneous parametric down-conversion. The atmospheric turbulence is modeled as a single-phase screen and simulated with spatial light modulators according to the theory of Kolmogorov. We find both theoretically and experimentally that the HOM dip is unaffected when only one of the photons passes through turbulence. When both photons pass through turbulence, the HOM interference is only slightly affected by the scintillation. The reasons behind these findings and their consequences for HOM-based teleportation are discussed.
The use of Higher-dimensional entangled systems have been proved to signi cantly improve many quantum in- formation tasks. For instance, it has been shown that the use of higher-dimensional entangled systems provides a higher information capacity and an increased security in quantum cryptography. The orbital angular momentum (OAM) state of light is a potential candidate for the implementation of higher-dimensional entangled systems and has thus been considered for free-space quantum communication. However, atmospheric turbulence severely affects the OAM state of photons. In this work, we study the evolution of the OAM entanglement between two qutrits (three-dimensional quantum systems) in atmospheric turbulence both numerically and experimentally. The qutrits are photons entangled in their orbital angular momentum (OAM) states generated by spontaneous parametric down conversion. We propagate one of the photons through turbulence while leaving the other undis- turbed. To compare our results with previous work, we simulate the turbulent atmosphere with a single phase screen based on the Kolmogorov theory of turbulence and we use the tangle to quantify the amount of entangle- ment between the two qutrits. We compare our results with the evolution of OAM entanglement between two qubits.
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.