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Verification of non-classical correlation in orbital angular momentum of photons without excess components

Yoko Miyamoto, Daisuke Kawase, Mitsuo Wada Takeda, Keiji Sasaki, Shigeki Takeuchi

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We propose a method to detect photons in superposition of orbital angular momentum (OAM) states using a hologram and path interferometer, and its application to verification of non-classical correlation in photon pairs. The method is free from excess OAM components, and a simple assumption of classical OAM correlation between the two photons removes contributions from excess components from the coincidence curve as well, even when the proposed method is used only on one of the photons.

DOI
10.1364/iqec.2011.i949

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We propose a method to detect photons in superposition of orbital angular momentum (OAM) states using a hologram and path interferometer, and its application to verification of non-classical correlation in photon pairs. The method is free from excess OAM components, and a simple assumption of classical OAM correlation between the two photons removes contributions from excess components from the coincidence curve as well, even when the proposed method is used only on one of the photons.
Detection of photons in orbital angular momentum (OAM) superposition states is crucial to verification of OAM entanglement. In the past this has been realized by laterally shifting a hologram designed to remove a charge 1 phase singularity at its center. Such a laterally shifted hologram converts a beam with an off-center singularity (similar to that created by superposing an m = 0 beam and an m = 1 beam, where in is the OAM mode number) into a Gaussian beam, which is then filtered through a single mode fiber (SMF). However, it has been shown that a photon detected by this method is not a simple superposition of a photon in the m = 0 Gaussian mode and the m = 1 mode detected with an unshifted hologram, making it necessary to apply complicated analysis. One problem is that the radial distributions of the detected m = 0 and 1 components as determined by the SMF change as the hologram is shifted. Another, possibly more serious problem is the mixing of other OAM components. To overcome this problem we propose a new scheme for the detection of OAM superposition states consisting of a hologram and a path interferometer. The hologram is designed so that the output is equally distributed between the 0th and 1st order diffraction beams. The 0th order is the input beam itself, whose m = 0 Gaussian component is filtered through an SMF. In the 1st order beam the m = 1 component is converted to m = 0 and is filtered through a second SMF. The filtered beams now have the same spatial distribution, and can be superposed by a beam splitter. By inserting attenuators and phase modulators within the interferometer, superpositions with varying amplitude ratios and relative phases can be detected without shifting the hologram.
We describe a simple experiment that is ideally suited to analyze the high-dimensional entanglement contained in the orbital angular momenta (OAM) of entangled photon pairs. For this purpose we use a two-photon interferometer with a built-in image rotator and measure the two-photon visibility versus rotation angle. Mode selection with apertures allows one to tune the dimensionality of the entanglement; mode selection with spiral phase plates and fibers allows detection of a single OAM mode. The experiment is analyzed in two different ways: either via the continuous two-photon amplitude function or via a discrete modal (Schmidt) decomposition of this function. The latter approach proves to be very fruitful, as it provides a complete characterization of the OAM entanglement.