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Optics Express

Amplitude damping of Laguerre-Gaussian modes

Angela L. Dudley, Michael Nock, Thomas Konrad, Filippus Stefanus Roux, Andrew Forbes

Published Oct 13, 2010• 9 citations
Publisher

Abstract

We present an amplitude damping channel for Laguerre-Gaussian modes. Our channel is tested experimentally for a Laguerre-Gaussian mode, having an azimuthal index l = 1, illustrating that it decays to a Gaussian mode in good agreement with the theoretical model for amplitude damping. Since we are able to characterize the action of such a channel on orbital angular momentum states, we propose using it to investigate the dynamics of entanglement.

DOI
10.1364/oe.18.022789

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We present an amplitude damping channel for Laguerre-Gaussian modes. Our channel is tested experimentally for a Laguerre-Gaussian mode, having an azimuthal index l = 1, illustrating that it decays to a Gaussian mode in good agreement with the theoretical model for amplitude damping. Since we are able to characterize the action of such a channel on orbital angular momentum states, we propose using it to investigate the dynamics of entanglement.
Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text A. Dudley, M. Nock, T. Konrad, F. S. Roux, and A. Forbes, "Mimicking an Amplitude Damping Channel for Laguerre Gaussian Modes," in Frontiers in Optics 2010/Laser Science XXVI, OSA Technical Digest (CD) (Optica Publishing Group, 2010), paper JWA58. Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article
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 is investigated in the Bessel-Gaussian (BG) basis. Having a readily adjustable radial scale, BG modes provide an alternative basis for OAM entanglement over Laguerre-Gaussian modes. We show that the OAM bandwidth in terms of BG modes can be increased by selection of particular radial wavevectors and leads to a flattening of the spectrum, which allows for higher dimensionality in the entangled state. We demonstrate entanglement in terms of BG modes by performing a Bell-type experiment and showing a violation of the Clauser-Horne-Shimony-Holt inequality for the ℓ = ±1 subspace. In addition, we use quantum state tomography to indicate higher-dimensional entanglement in terms of BG modes.
Two different experimental techniques for preparing and analysing superpositions of Gaussian and Laguerre–Gaussian modes are presented. These involve exploiting an interferometric method in one case and using computer-generated holograms in the other. It is shown that by shifting a hologram with respect to an incoming Gaussian beam, different superpositions of the Gaussian and the Laguerre–Gaussian beam can be produced. An analytical expression connecting the relative phase, the amplitudes of the modes and the displacement of the hologram is given. The application of such orbital angular momenta superpositions in quantum experiments such as quantum cryptography is discussed.