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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Atmospheric turbulence and free-space optical communication using orbital angular momentum of single photons

Carl Paterson

Published Nov 11, 2004• 16 citations
Publisher

Abstract

The well defined spin and orbital angular momentum states of photons offers 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 wavefunction and the number of orbital angular momentum eigenstates is unlimited, giving the possibility of arbitrary base-N digits. In this paper, free-space optical communications using angular momentum states of single photons is investigated and in particular the effect of atmospheric turbulence on the angular momentum of the photons is modelled. 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. By considering the resulting wave as a superposition of angular momentum states, the probability of obtaining correct or incorrect measurements of the transmitted digit is calculated. The effect on a free-space optical communication using orbital angular momentum and the use of adaptive optics is discussed. The information capacity per photon is quantified and compared to that using polarization states for binary digits.

DOI
10.1117/12.565435

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The well defined spin and orbital angular momentum states of photons offers 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 wavefunction and the number of orbital angular momentum eigenstates is unlimited, giving the possibility of arbitrary base-N digits. In this paper, free-space optical communications using angular momentum states of single photons is investigated and in particular the effect of atmospheric turbulence on the angular momentum of the photons is modelled. 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. By considering the resulting wave as a superposition of angular momentum states, the probability of obtaining correct or incorrect measurements of the transmitted digit is calculated. The effect on a free-space optical communication using orbital angular momentum and the use of adaptive optics is discussed. The information capacity per photon is quantified and compared to that using polarization states for binary digits.
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.
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.
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.
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.
The effects of propagation through random aberrations on coherence for single-photon communication systems based on orbital angular momentum states are quantified. A rotational coherence function is derived which leads to scattering equations for azimuthal modes of different orbital angular momentum states. The effect on a single-photon communication system is quantified using the channel capacity. The work shows that the decoherence effect of atmospheric turbulence on such systems is important even for weak turbulence.
Quantum key distribution is a promising candidate to ensure secure communication in the future. Higher-dimensional state spaces as provided by the orbital angular momentum of photons (OAM) could further improve the security and robustness to noise. When transmitted through free-space, these photons experience atmospheric turbulence which introduces distortions to the encoded OAM. A technologoy called adaptive optics has been developed in astronomy to counter-act turbulence-induced distortion. While the application of adaptive optics has been considered in the context of classical OAM communication, this thesis presents the first results for OAM-based quantum key distribution. The main result of this thesis is that the losses of the quantum mechanical properties of OAM photons in atmospheric can be mitigated by adaptive optics. Both the entanglement and the trace of the final state's density matrix can be significantly improved. Furthermore, the security of the quantum key distribution protocol can be ensured for two to three times stronger turbulence as measured by the Fried parameter. The presented results demonstrate the great potential of adaptive optics for OAM quantum cryptography.