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arXiv:2109.08035 · Physical Review A

Talbot self-imaging and two-photon interference in ring-core fibers

Matias Eriksson, Benjamin A. Stickler, Lea Kopf, Markus Hiekkamäki, Regina V. Gumenyuk, Yuri Chamorovskiy, Sven Ramelow, Robert Fickler

Published Dec 15, 2021• 6 citations
arXivHTMLPDF

Abstract

Wave propagation on the surface of cylinders exhibits interferometric self-imaging, much like the Talbot effect in the near-field diffraction at periodic gratings. We report the experimental observation of the cylindrical Talbot carpet in weakly guiding ring-core fibers for classical light fields. We further show that the ring-core fiber acts as a higher-order optical beamsplitter for single photons, whose output can be controlled by the relative phase between the input light fields. By also demonstrating high-quality two-photon interference between indistinguishable photons sent into the ring-core fiber, our findings open the door to applications in optical telecommunications as a compact beam multiplexer as well as in quantum information processing tasks as a scalable realization of a linear optical network.

DOI
10.1103/physreva.104.063512

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Wave propagation on the surface of cylinders exhibits interferometric self-imaging, much like the Talbot effect in the near-field diffraction at periodic gratings. We report the experimental observation of the cylindrical Talbot carpet in weakly guiding ring-core fibers for classical light fields. We further show that the ring-core fiber acts as a higher-order optical beamsplitter for single photons, whose output can be controlled by the relative phase between the input light fields. By also demonstrating high-quality two-photon interference between indistinguishable photons sent into the ring-core fiber, our findings open the door to applications in optical telecommunications as a compact beam multiplexer as well as in quantum information processing tasks as a scalable realization of a linear optical network.
The generation and manipulation of single- and multi-photon states play a central role in numerous quantum optics applications, including quantum communication, imaging, sensing, and information processing. The transverse spatial degrees of freedom of photons are particularly attractive because they provide access to high-dimensional quantum states. Optical systems that inherently support spatially structured modes therefore provide compact and versatile platforms for manipulating such states. Ring-core fibers naturally support azimuthal modes whose interference produces cylindrical Talbot self-imaging. At half the Talbot length, this propagation performs a transformation analogous to that of a balanced beam splitter between diametrically opposite angular positions. In this thesis, the cylindrical Talbot effect is experimentally investigated using the full transverse output of a spontaneous parametric down conversion source, with the goal of observing two-photon interference occurring inside a ring-core fiber. Degenerate photon pairs were generated in a periodically poled potassium titanyl phosphate crystal. The transverse momentum anti-correlations of the generated photons were determined with a single-photon avalanche diode camera utilizing the reconstructed joint probability distributions from sequences of short-exposure frames. Near- and far field measurements after the nonlinear crystal verified the expected transverse momentum anti-correlations and transverse position correlation properties of the generated biphoton state. The annular far field distribution was subsequently shaped and coupled into a ring-core fiber with a length corresponding to half of the cylindrical Talbot length. Intensity acquisitions at the fiber output confirmed the expected beam splitting of an angularly localized input distribution into two diametrically opposite outputs. Two-photon interference was investigated at discrete temporal delays by observing the coincidence counts between opposite output ports of the ring-core fiber. No reduction in coincidences between opposite outputs was observed at zero temporal delay. The statistical uncertainty, poor signal-to-noise ratio, and deviation from the correct Talbot length most likely prevent the observation of the interference effect. The correlation structure of the biphoton state after the fiber was likewise insufficient to determine an expected transformation from momentum anti-correlation to correlation. These results establish that the cylindrical Talbot effect can be employed for manipulating the spatial output of an SPDC source to observe beam splitting. The two-photon interference measurements can be utilized for identifying the main experimental limitations affecting the visibility of the observed effect. These results provide a framework for further investigations of the cylindrical Talbot effect for compact beam splitting and quantum state manipulation.
Talbot and Talbot-Lau effects are frequently used in lensless imaging applications with light, ultrasound, x-rays, atoms and molecules--generally in situations where refractive optical elements are non-existent or not suitable. We here show an experimental visualization of the intriguing wave patterns that are associated with near-field interferometry behind a single periodic diffraction grating under plane wave illumination and which are often referred to as Talbot carpets or quantum carpets. We also show the patterns behind two separated diffraction gratings under nearly-monochromatic but spatially incoherent illumination that illustrate the nature of Talbot-Lau carpets.
Single-photon interference due to passage through a periodic grating is considered in a novel proposal for processing DDD-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free-space propagation naturally implements basic single-quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near-field diffraction regime. By adding a diagonal phase gate, we show that a complete set of single-quDit gates can be implemented. We then introduce a spatially dependent beam splitter that allows for projective measurements in the computational basis and can be used for the implementation of controlled operations between two quDits. Universal quantum information processing can then be implemented with linear optics and ancilla photons via postselection and feed-forward following the original proposal of Knill-Laflamme and Milburn. Although we consider photons, our scheme should be directly applicable to a number of other physical systems. Interpretation of the Talbot effect as a quantum logic operation provides a beautiful and interesting way to visualize quantum computation through wave propagation and interference.
We report the first experimental observation of quantum Talbot effects with single photons and entangled photon pairs. Both the first- and second-order quantum Talbot self-images are observed experimentally. They exhibit unique properties, which are different from those produced by coherent and incoherent classical light sources. In particular, our experiments show that the revival distance of two-photon Talbot imaging is twice the usual classical Talbot length and there is no net improvement in the resolution, due to the near-field effect of Fresnel diffraction, which is different from the case of previous proof-of-principle quantum lithography experiments in the far field.
Nearly two centuries ago Talbot first observed the fascinating effect whereby light propagating through a periodic structure generates a `carpet' of image revivals in the near field. Here we report the first observation of the spatial Talbot effect for light interacting with periodic Bose-Einstein condensate interference fringes. The Talbot effect can lead to dramatic loss of fringe visibility in images, degrading precision interferometry, however we demonstrate how the effect can also be used as a tool to enhance visibility, as well as extend the useful focal range of matter wave detection systems by orders of magnitude. We show that negative optical densities arise from matter-wave induced lensing of detuned imaging light -- yielding Talbot-enhanced single-shot interference visibility of >135% compared to the ideal visibility for resonant light.
Nearly two centuries ago Talbot first observed the fascinating effect whereby light propagating through a periodic structure generates a ‘carpet’ of image revivals in the near field. Here we report the first observation of the spatial Talbot effect for light interacting with periodic Bose-Einstein condensate interference fringes. The Talbot effect can lead to dramatic loss of fringe visibility in images, degrading precision interferometry, however we demonstrate how the effect can also be used as a tool to enhance visibility, as well as extend the useful focal range of matter wave detection systems by orders of magnitude. We show that negative optical densities arise from matter-wave induced lensing of detuned imaging light – yielding Talbot-enhanced single-shot interference visibility of > 135% compared to the ideal visibility for resonant light.