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Jiguang zazhi

The effects of atmospheric turbulence on entangled orbital angular momentum of single photons for slant quantum communication

Jian Zhang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

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.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 1, 2011•0 citations
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.
The effect of atmospheric turbulence on quantum optical communication systems based on angular momentum states of single photons is investigated and the detection probabilities of the orbital angular momentum of the photons propagation in slant atmospheric turbulence channel is modeled with Rytov approximation and modified von Karman spectrum model of index-of-refraction fluctuation.The statistical averaging of the orbital angular momentum  of single photon in quantum communication channel is given.
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 well defined orbital angular momentum states of photons offer a practical realization of quantum digits and a means of secure single-photon optical communication. The orbital angular momentum is associated with the spatial distribution of the wave function and the number of orbital angular momentum eigenstates is unlimited, giving the possibility of arbitrary base-N digits. The free-space optical communications using angular momentum states of single photons is investigated and the effect of slant path atmospheric turbulence on the angular momentum of the photons is modeled with Rytov approximation and modified von Karman spectrum model of index-of-refraction fluctuation. The analytical modeling for the angular momentum scattering due to the atmospheric turbulence and the orbital angular momentum quantum number for photons propagation in slant path atmospheric turbulence are presented. The refractive index fluctuations in the atmosphere perturb the complex amplitude of a propagating beam so that the photons that were launched in an eigenstate of orbital angular momentum are no longer guaranteed to be in the original eigenstate after propagation.
We extend the theory of detection probabilities of single-photon communication in turbulent atmosphere to the entangled case and derive analytical expressions for detection probabilities. We show that the rotational field correlation in the entangled case cannot be expressed as a straightforward extension from the disentangled case. By considering the orbital angular momentum (OAM) entangled Laguerre-Gaussian (LG) beams for illustration, we explore the effect of non-Kolmogorov atmospheric turbulence on the probabilities of both the biphoton detection and the single-photon detection. The entanglement of OAM LG beams contributes positively to the faithful detection probability. The change of maximal crosstalk probability in the detection process is also explored, which displays the non-linear dependence on the crosstalk quantum number.
Based on Zernike-model expansion of turbulence phase aberrations and non-Kolmogorov spectrum model of index-of-refraction fluctuation, we analyze the effects of low-order Zernike turbulence aberrations on orbital angular momentum (OAM) entanglement states in a weak fluctuation region. The signal photon detection probability of OAM entanglement states propagating in a slant turbulence channel with non-Kolmogorov turbulence Z-tilt, defocus, astigmatism, and coma aberrations are modeled, respectively. The results demonstrate that turbulence Z-tilt aberration is the dominant aberration, coma is the second, and astigmatism is the third, but that the defocus aberration has no impact on the detection probability. As the power-law exponent of the non-Kolmogorov spectrum increases from 3 to 4, the detection probability decreases.
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.