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Journal of Marine Science and Engineering

Bi-Photon Entangled Airy Beams through Unstable Oceanic Turbulence

Donghui Yang, Yu Zhou, Zheng-Da Hu, Wenhai Wang, Yun Zhu

Published Oct 31, 2022• 3 citations
Publisher

Abstract

Orbital angular momentum (OAM) carried by bi-photon entangled Airy beams in unstable oceanic turbulence is theoretically investigated. The analytical expression of the spatial coherence radius of a spherical wave in the unstable stratification oceanic turbulence is derived to obtain the relative detection probability of bi-photon entangled Airy beams. The relative detection probability of OAM carried by bi-photon entangled Airy beams acquires significant enhancements—up to 62% compared to the same measurement for the single photon system over a distance of 100 m. Lower-order bi-photon entangled Airy beams with larger wavelengths, and main ring radius are less affected by oceanic turbulence. A larger main ring radius also contributes to reducing the fluctuations in detection probability. Oceanic turbulence dominated by salinity fluctuations induces more adverse effects on the OAM, as well as a stronger strength of the turbulence.

DOI
10.3390/jmse10111604

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Orbital angular momentum (OAM) carried by bi-photon entangled Airy beams in unstable oceanic turbulence is theoretically investigated. The analytical expression of the spatial coherence radius of a spherical wave in the unstable stratification oceanic turbulence is derived to obtain the relative detection probability of bi-photon entangled Airy beams. The relative detection probability of OAM carried by bi-photon entangled Airy beams acquires significant enhancements—up to 62% compared to the same measurement for the single photon system over a distance of 100 m. Lower-order bi-photon entangled Airy beams with larger wavelengths, and main ring radius are less affected by oceanic turbulence. A larger main ring radius also contributes to reducing the fluctuations in detection probability. Oceanic turbulence dominated by salinity fluctuations induces more adverse effects on the OAM, as well as a stronger strength of the turbulence.
The propagation properties of Laguerre-Gaussian beams in oceanic turbulence are investigated for both single-photon and biphoton cases. For single-photon communication, the channel capacity and trace distance are employed, both of which effectively reveal the communication performance via different viewpoints. For the biphoton case, we consider distributions of quantum resources including entanglement and quantum coherence. Turbulence conditions with a larger inner-scale and anisotropic factors, higher dissipation rate of kinetic energy, lower dissipation rate of the mean-squared temperature, and lower temperature-salinity contribution ratio combined with longer wavelength and an appropriate range of optimal beam width are beneficial to communication performances. Our results provide theoretical significance to improve the orbital-angular-momentum communication via oceanic turbulence.
The effect of the turbulent motion of ocean on the quantum communication based on the orbital angular momentum in an underwater quantum channel is studied in this work. Based on the power spectrum model of ocean turbulence proposed by Elamassie, the quantitative relationships of different ocean turbulence parameters with the single photon detection probability of orbital angular momentum photons, the channel capacity, the key generation rate, the concurrence of two entangled photons are proposed. The maximum entanglement distance of the orbital angular momentum entangled photon-pairs in the ocean turbulence is further studied by the universal entanglement decay of the concurrence of entangled photon-pairs in the ocean turbulence. The results show that the detection probability of single photon, the channel capacity, the key generation rate, and the concurrence of entangled photon-pairs decrease with the increase of the dissipation rate of turbulent kinetic energy and the decrease of the rate of dissipation of mean-squared temperature. The influence of the temperature and salinity balance parameter of ocean turbulence on the performance of underwater quantum communication are significantly different under the condition of whether the stable stratification of seawater is assumed or not. In the ocean turbulent environment, the increasing of the initial orbital angular momentum quantum number of signal photons can improve the key generation rate of quantum key distribution and the resistance of entangled photons to entanglement decay.
Orbital angular momentum (OAM) entangled bi-photons are a resource for the higher dimensional implementation of quantum cryptography, which allows secure communication over various channels. In the case where free-space is used as communication channel the initial OAM entangled bi-photon loses some or even all of its entanglement because of the scintillation that it experiences while propagating through the turbulence in the atmosphere. This decoherence of OAM entanglement has so far only been studied for the case of weak turbulence. Unfortunately, it is the more challenging strong turbulence scenario that is relevant for the practical implementation of free-space quantum communication through the atmosphere. Using an approach that differs from previous approaches, we derive a master equation for the evolution of an OAM entangled bi-photon during propagation through turbulence. However, in our approach the equation contains a derivative with respect to the propagation distance instead of time. The principle is to consider the propagation over an infinitesimal distance of OAM basis states through a random medium. This approach allows one to include, not only the effect of turbulence of arbitrary strength, but also the effect of the inner and outer scale of the turbulence, as represented by the Tartarskii and von Karman spectra. The resulting expression can predict the rates of decoherence for arbitrary initial OAM entangled states and can be used to calculate the concurrence, which measures the amount of entanglement, as a function of propagation distance for different initial entangled OAM states.
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 offects of the atumospheric turbutence on z-tilt corrected or beam center tracked entangled orbital angular momentum(OAM)states generated by parametric down conversion and propagation in atmospheric communication channel are studied,and the entangled orbital angular momentum states detection probabilities of signal photon which are propagation in slant atmospheric turbulence and include the z-tilt corrected or beam center tracked phase fluctuation and amplitude fluctuation caused by atmospheric turbulence are modelled.The joint detection probabilities of OAM state entangled photons versus propagationdistance for the zenith angle θ=π/6 and θ=π/3 are calculated numerically.The results demonstrate that when propagation distance z 500m,the joint detection probability of entangled photons decays rapidly as propagation distance increases,but when propagation distance z1000m,the decay-rate of the joint detection probability of entangled photons is vary small as propagation distance increases.It is shown that the joint detection probabilities of entangled photons with lower total OAM decay less rapidly than those with higher OAM values.It is also found that the joint detection probabilities of entangled photons with smaller zenith angle decay less rapidly than those with larger zenith angle.
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.