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arXiv:1612.02552

Recovering Quantum Information in Orbital Angular Momentum of Photons by Adaptive Optics

José Raúl González Alonso, Todd A. Brun

Published Dec 8, 2016• 0 citations
arXivHTMLPDF

Abstract

Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. We explore the ability of adaptive optics to compensate for this disturbance by measuring and correcting cumulative phase shifts in the wavefront. These shifts can be represented as a sum of Zernike functions; we analyze the residual errors after correcting up to a certain number of Zernike modes when an orbital angular momentum state is transmitted through a turbulent atmosphere whose density fluctuations have a Kolmogorov spectrum. We approximate the superoperator map that represents these residual errors and find the solution in closed form. We illustrate with numerical examples how this perturbation depends on the the number of Zernike modes corrected and the orbital angular momentum state of the light.

DOI
10.48550/arxiv.1612.02552

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Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. We explore the ability of adaptive optics to compensate for this disturbance by measuring and correcting cumulative phase shifts in the wavefront. These shifts can be represented as a sum of Zernike functions; we analyze the residual errors after correcting up to a certain number of Zernike modes when an orbital angular momentum state is transmitted through a turbulent atmosphere whose density fluctuations have a Kolmogorov spectrum. We approximate the superoperator map that represents these residual errors and find the solution in closed form. We illustrate with numerical examples how this perturbation depends on the the number of Zernike modes corrected and the orbital angular momentum state of the light.
Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. Understanding the noise processes that affect photons is essential if we desire to protect them. In this paper we use the infinitesimal propagation equation of Roux to derive a discrete Lindblad equation, and numerically study the form of the most relevant Lindblad operators. We find that the dominant Lindblad operators are those that shift the angular momentum by one unit. We explore possible schemes to protect quantum information across multiple photons by concatenating a standard quantum error-correcting code with an error-detecting code for orbital angular momentum.
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Orbital angular momentum modes are a common choice for higher-dimensional encoding of photonic qubits. When transported across large distances, these qubits (or qudits) will pass through atmospheric turbulence and suffer aberrations leading to qubit errors, information loss, entanglement degradation, and loss of quantum behavior. In order to quantify some of these effects, we have developed an atmospheric turbulence emulator which allows us to finely control parameters that determine turbulence strength. In this paper, we describe our turbulence emulator and our methods of coupling orbital angular momentum qubits into the system. We present a quantitative demonstration of the degradation of classical orbital angular momentum modes in turbulence. Finally, we discuss ongoing efforts to measure the loss of quantum behavior in orbital angular momentum qubits due to atmospheric turbulence and the use of adaptive optics to mitigate some of the negative effects of atmospheric turbulence.
The orbital angular momentum (OAM) of photons is a promising degree of freedom for high-dimensional quantum key distribution (QKD). However, effectively mitigating the adverse effects of atmospheric turbulence is a persistent challenge in OAM QKD systems operating over free-space communication channels. In contrast to previous works focusing on correcting static simulated turbulence, we investigate the performance of OAM QKD in real atmospheric turbulence with real-time adaptive optics (AO) correction. We show that even though our AO system provides a limited correction, it is possible to mitigate the errors induced by weak turbulence and establish a secure channel. The crosstalk induced by turbulence and the performance of AO systems is investigated in two configurations: a lab-scale link with controllable turbulence, and a 340 m long cross-campus link with dynamic atmospheric turbulence. Our experimental results suggest that an advanced AO system with fine beam tracking, reliable beam stabilization, precise wavefront sensing, and accurate wavefront correction is necessary to adequately correct turbulence-induced error. We also propose and demonstrate different solutions to improve the performance of OAM QKD with turbulence, which could enable the possibility of OAM encoding in strong turbulence.
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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.