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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Born's rule and single-photon diffraction by a triangular slit

J. Miguel Hickmann, E. J. S. Fonseca, Alcenísio J. Jesus‐Silva

Published May 1, 2011• 0 citations
Publisher

Abstract

The double-slit at single photon or electron level is the ubiqutous quantum interference experiment with the path phase playing a key role. On the other hand, photon's orbital angular momentum (OAM) brings a new dimension to interference problems with the spiral phase degree of freedom. In this work, we use OAM's two dimensional properties to extended the double-slit to a triple-slit configuration in the shape of an equilateral triangle, obtaining a triangular latticed single-photon counting interference pattern. In order to understand this interference pattern in terms of wave-particle duality, we have to take into account that, in contrast with the parallel double and triple slit cases, the azimuthal phase also plays a fundamental role, being undistinguishable from path phase.

DOI
10.1109/cleoe.2011.5943383

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The double-slit at single photon or electron level is the ubiqutous quantum interference experiment with the path phase playing a key role. On the other hand, photon's orbital angular momentum (OAM) brings a new dimension to interference problems with the spiral phase degree of freedom. In this work, we use OAM's two dimensional properties to extended the double-slit to a triple-slit configuration in the shape of an equilateral triangle, obtaining a triangular latticed single-photon counting interference pattern. In order to understand this interference pattern in terms of wave-particle duality, we have to take into account that, in contrast with the parallel double and triple slit cases, the azimuthal phase also plays a fundamental role, being undistinguishable from path phase.
We use photon OAM's two-dimensional properties to extend the double-slit to a two-dimensional triple-slit configuration in the shape of an equilateral triangle, obtaining a bidimensional triangular interference pattern at photon level, whose size depends on the OAM amount. We also show that for this pattern, in contrast with the parallel two- and three-slit cases, the azimuthal phase plays a fundamental role, being undistinguishable from the path phase. Our results confirm that only pairs, here associated to path and azimuthal phases, contribute to the two-dimensional photon detection probability, as established by Born's rule.
This work presents a single-pass diffraction experiment that demonstrates that single photons in a vortex beam in passing through three slits arranged in an equilateral triangle can interfere with themselves and provide quantitative information of their total amount of orbital angular momentum (OAM) they carry. For the experiment presented the aperture has been reduced to a very thin triangular slit. A vortex beam is created by a diffractive optical element (DOE) and then it is made to pass through the slit. This work is considered as an extension to the Young double slit experiment.
Optical orbital angular momentum (OAM) is a special property of photons and has evoked research onto the light–matter interaction in both classical and quantum regimes. In classical optics, OAM is related to an optical vortex with a helical phase structure. In quantum optics, photons with a twisted or helical phase structure will carry a quantized OAM. To our knowledge, however, so far, no experiment has demonstrated the fundamental property of the OAM at the single-photon level. In this Letter, we have demonstrated the average photon trajectories of twisted photons in a double-slit interference. We have experimentally captured the double-slit interference process of twisted photons by a time-gated intensified charge-coupled device camera, which is trigged by a heralded detection. Our work provides new perspectives for understanding the micro-behaviors of twisted particles and enables new applications in imaging and sensing.
We demonstrate that by diffracting light at single photon level with orbital angular momentum (OAM) by an equilateral triangular aperture, it is possible to determine their OAM amount by simply counting the number of maxima in the side of a generated triangular shaped hexagonal lattice in the spatial photon probability distribution. The sign of the OAM is obtained by the orientation of the latticed triangle. We also show that by changing the aperture size it is possible to discriminate OAM state superpositions.
Youngs double slit experiment is one of the most celebrated achievements in quantum and classical optics; it provides experimental proof of the wave-particle duality of light. When the paths of the double slit are marked with orthogonal polarizations, the path information is revealed and no interference pattern is observed. However, the path information can be erased with a complimentary analysis of the polarization. Here we use hybrid entanglement between photons carrying orbital angular momentum and polarization to show that, just as in Young's experiment, the paths (OAM) marked with polarization do not lead to interference. However, when introducing the eraser (polarizer) which projects the polarization of one of the entangled photons onto a complementary polarization basis, the OAM (paths) are allowed to interfere, leading to the formation of azimuthal fringes whose frequency is proportional to the OAM content carried by the photon.