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arXiv:2011.14702 · Physical Review Applied

Vector-Mode Decay in Atmospheric Turbulence: An Analysis Inspired by Quantum Mechanics

Isaac M. Nape, Nikiwe Mashaba, Nokwazi Mphuthi, Sruthy Jayakumar, Shanti Bhattacharya, Andrew Forbes

Published Mar 10, 2021• 13 citations
arXivHTMLPDF

Abstract

Vector beams are inhomogeneously polarized optical fields with nonseparable quantumlike correlations between their polarization and spatial components, and they hold tremendous promise for classical and quantum communication across various channels, e.g., the atmosphere, underwater, and in optical fiber. Here, we show that by exploiting their quantumlike features by virtue of the nonseparability of the field, the decay of both the polarization and spatial components can be studied in tandem. In particular, we invoke the principle of channel-state duality to show that the degree of nonseparability of any vector mode is purely determined by that of a maximally nonseparable one, which we confirm using orbital angular momentum (OAM) as an example for topological charges of $\ensuremath{\ell}=1$ and $\ensuremath{\ell}=10$ in a turbulent atmosphere. A consequence is that the well-known cylindrical vector vortex beams are sufficient to predict the behavior of all vector OAM states through the channel. Our method reveals interesting features about the performance of various modes through the channel: the decay in vector quality decreases with an increasing OAM value, even though the spread is higher for larger OAM modes. Our approach offers a fast and easy probe of noisy channels, while at the same time revealing the power of quantum tools applied to classical light.

DOI
10.1103/physrevapplied.15.034030

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Vector beams are inhomogeneously polarized optical fields with nonseparable quantumlike correlations between their polarization and spatial components, and they hold tremendous promise for classical and quantum communication across various channels, e.g., the atmosphere, underwater, and in optical fiber. Here, we show that by exploiting their quantumlike features by virtue of the nonseparability of the field, the decay of both the polarization and spatial components can be studied in tandem. In particular, we invoke the principle of channel-state duality to show that the degree of nonseparability of any vector mode is purely determined by that of a maximally nonseparable one, which we confirm using orbital angular momentum (OAM) as an example for topological charges of \ensuremathℓ=1\ensuremath{\ell}=1\ensuremathℓ=1 and \ensuremathℓ=10\ensuremath{\ell}=10\ensuremathℓ=10 in a turbulent atmosphere. A consequence is that the well-known cylindrical vector vortex beams are sufficient to predict the behavior of all vector OAM states through the channel. Our method reveals interesting features about the performance of various modes through the channel: the decay in vector quality decreases with an increasing OAM value, even though the spread is higher for larger OAM modes. Our approach offers a fast and easy probe of noisy channels, while at the same time revealing the power of quantum tools applied to classical light.
Orbital angular momentum (OAM) multiplexing provides an infinite-dimensional discrete Hilbert space ideally suited for high-capacity free-space quantum key distribution (QKD). Nevertheless, pure scalar spatial modes carrying topological charge (∣ℓ∣≥1|\ell| \ge 1∣ℓ∣≥1) undergo severe decoherence when transmitted through terrestrial atmospheric turbulence. Turbulent refractive-index eddies split high-order vortex singularities, induce catastrophic intermodal crosstalk across adjacent topological channels, and rapidly drive the quantum bit error rate (QBER) well above the unconditional 11% security threshold associated with individual cloning attacks. Here, we demonstrate that hybrid polarization-OAM entangled states, known as vector vortex beams (VVBs), provide intrinsic, hardware-free immunity against turbulent perturbations. Because the optical anisotropy of terrestrial air is exceedingly small (Δn<10−9Δn < 10^{-9}Δn<10−9), refractive-index fluctuations couple symmetrically to orthogonal circular polarization modes as an identical common-mode scalar phase screen that cancels in the relative polarization-phase degree of freedom. By numerically propagating modal fields through modified power-spectral phase screens over turbulence strengths ranging from D/r0=0D/r_0 = 0D/r0​=0 to 3.03.03.0, we show that the VVB encoding protocol suppresses the asymptotic QBER from 42.0% to 4.8%, yielding an error-suppression factor of approximately 11.6 without requiring active adaptive optics or deformable mirrors.
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.
Vector vortex beams are structured states of light that are nonseparable in their polarisation and spatial mode, they are eigenmodes of free-space and many fiber systems, and have the capacity to be used as information carriers for both classical and quantum communication. Here, we outline recent progress in our understanding of these modes, from their creation to their characterization and detection. We then use these tools to study their propagation behavior in free-space and optical fiber and show that modal cross-talk results in a decay of vector states into separable scalar modes, with a concomitant loss of information. We present a comparison between probabilistic and deterministic detection schemes showing that the former, while ubiquitous, negates the very benefit of increased dimensionality in quantum communication while reducing signal in classical communication links. This work provides a useful introduction to the field as well as presenting new findings and perspectives to advance it further.
Orbital angular momentum (OAM) entanglement gives access to multiple qubit and high dimensional Hilbert spaces, but is unfortunately susceptible to disturbance, decaying in real-world noisy channels. Here, we show there is an underlying topology arising from OAM entanglement that is robust to such channels, which we demonstrate using atmospheric turbulence -- exemplary of stochastic or chaotic media. Using a quantum channel with various turbulence strengths, we find the OAM topological observable preserved even though the OAM itself is shown to be highly sensitive to the turbulence. We show this is true for mixed states too, with the OAM topology intact even as the purity of the state decreases due to decoherence. Our work offers a new perspective on OAM entanglement preservation, and may easily be extended to other spatial bases, degrees of freedom, as well as complex channels, whether static or dynamic.
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.
Orbital angular momentum (OAM) entanglement gives access to multiple qubit and high dimensional Hilbert spaces but is unfortunately susceptible to disturbance, decaying in real-world noisy channels. Here, we show that an underlying topology arising from OAM entanglement remains robust to such channels, which we demonstrate using atmospheric turbulence-exemplary of stochastic or chaotic media. Using a quantum channel with various turbulence strengths, we find that the OAM topological observable is preserved even though the OAM itself is shown to be highly sensitive to the turbulence. We show this is true for mixed states too, with the OAM topology intact even as the purity of the state decreases due to decoherence. Our Letter offers a new perspective on harnessing OAM entanglement in noisy channels, and may easily be extended to other spatial bases, degrees of freedom, and complex channels.