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Physical Review A

Unusual quantum Talbot effect based on the orbital angular momentum of photons

Yifan Sun, Xiangdong Zhang

Published Jun 27, 2016• 6 citations
Publisher

Abstract

The quantum Talbot effects with orbital angular momentum (OAM) photons have been investigated theoretically. Two schemes, holographic ghost-image and twin-photon configuration, have been considered. They exhibit unique properties, which are different from the cases of previous classical and quantum Talbot effects. The Talbot effects in the present schemes originate from lateral translation of the periodic object instead of transverse coherences of optical fields or photon wave functions. The Talbot pattern in the present case can be manipulated by the OAM number of the incident photons, which is equivalent to the Talbot effect of an effective periodic object illuminated by photons without the OAM. This means that complex diffraction patterns of an unusual periodic object can be obtained by designing the Talbot effect with OAM photons, which provides a promising idea in optical designs for the diffraction patterns.

DOI
10.1103/physreva.93.063851

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•Sep 19, 2019•0 citations
The quantum Talbot effects with orbital angular momentum (OAM) photons have been investigated theoretically. Two schemes, holographic ghost-image and twin-photon configuration, have been considered. They exhibit unique properties, which are different from the cases of previous classical and quantum Talbot effects. The Talbot effects in the present schemes originate from lateral translation of the periodic object instead of transverse coherences of optical fields or photon wave functions. The Talbot pattern in the present case can be manipulated by the OAM number of the incident photons, which is equivalent to the Talbot effect of an effective periodic object illuminated by photons without the OAM. This means that complex diffraction patterns of an unusual periodic object can be obtained by designing the Talbot effect with OAM photons, which provides a promising idea in optical designs for the diffraction patterns.
The self-imaging, or Talbot effect, that occurs with the propagation of periodically structured waves has enabled several unique applications in optical metrology, image processing, data transmission, and matter-wave interferometry. In this paper, we report on a demonstration of a Talbot effect with single photons prepared in a lattice of orbital angular momentum (OAM) states. We observe that upon propagation the wavefronts of the single photons manifest self-imaging whereby the OAM lattice intensity profile is recovered. Furthermore, we show that the intensity at fractional Talbot distances is indicative of a periodic helical phase structure corresponding to a lattice of OAM states. This phenomenon is a powerful addition to the toolbox of orbital angular momentum and spin-orbit techniques that have already enabled many recent developments in quantum optics.
The Talbot effect, a wave-optical self-imaging phenomenon originally observed in real-space, has developed into a powerful framework for programmable modal transformations across diverse physical platforms. Here, we report the experimental demonstration of nonlocal Talbot transformations within a high-dimensional, orbital angular momentum (OAM) entangled two-photon system. By exploiting the intrinsic nonlocal correlations generated through spontaneous parametric down-conversion, we show that applying an azimuthal Talbot phase on one photon of an entangled pair is sufficient to coherently reshape the OAM modal distribution of its spatially separated partner, without any direct local operation on the latter. As a proof of principle, we further demonstrate the inverse Talbot transformation within the same platform by incorporating the required quadratic phase during the state-preparation stage. These results extend Talbot physics from local mode manipulation to entanglement-assisted nonlocal transformations in a high-dimensional discrete basis. The demonstrated platform opens versatile routes toward conditional remote OAM-mode conversion, structured entangled-state engineering, and high-dimensional quantum information processing.
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.
The second-order Talbot effect is analyzed for a periodic object illuminated by entangled photon pairs in both the quantum imaging and quantum lithography configurations. The Klyshko picture is applied to describe the quantum imaging scheme, in which self-images of the object that may or may not be magnified can be observed nonlocally in the photon coincidences but not in the singles count rate. In the quantum lithography setup, we find that the second-order Talbot length is half that of the classical first-order case, thus the resolution may be improved by a factor of 2.
The angular profile and the orbital angular momentum of a light mode are related by Fourier transform. Any modification of the angular distribution, e. g. via diffraction off a suitably programmed spatial light modulator, influences the orbital angular momentum spectrum of the light. This holds true even at the single photon level. We observe the influence of various angular masks on the orbital angular momentum spectrum, both in the near and the far field, and describe the resulting patterns in terms of angular diffraction. If photons are entangled in their orbital angular momentum, diffraction of one photon affects the orbital angular momentum spectrum of its partner photon, and angular ghost diffraction can be measured in the coincidence counts. We highlight the role of the angular Fourier relationship for these effects.
The thesis introduces two single-photon experiments with the lattice of spin-orbit arrays. The basic background knowledge has been introduced in Chapter 1. Chapters 2-4 describe the detailed techniques used in these two experiments. \n \nIn the first work, we implement a remote state preparation protocol on our single-photon orbital angular momentum (OAM) lattice state via hybrid-entanglement. Remote state preparation is a variant of quantum state teleportation where the sender knows the transmitted state. It is known to require fewer classical resources and exhibit a nontrivial trade-off between the entanglement and classical communication compared with quantum teleportation. Here we propose a state preparation scheme between two spatially separated photons sharing a hybrid-entangled polarization-OAM state. By sending one of the polarization-entangled photon pairs through Lattice of Optical Vortex prism pairs, we generate a two-dimensional lattice of spin-orbit coupled single-photons. We show that the measurement taken by an electron-multiplying intensified CCD camera on the transformed photons can be remotely prepared by the polarization projection of the other. Our protocol could have a significant impact on long-distance quantum communication with higher channel capacity and lead to more efficient and compatible quantum information processing techniques. \n \nThe second experiment investigates the single-photon Talbot Effect in spin-orbit arrays. The Talbot Effect is a near-field diffraction effect, that occurs with the propagation of periodically structured waves. It has enabled several unique applications in optical metrology, image processing, data transmission, and matter-wave interferometry. We observe that upon propagation, the wavefronts of the single photons manifest self-imaging whereby the OAM lattice intensity profile is recovered. Furthermore, we show that the intensity distribution at each fractional Talbot distance is indicative of the periodic helical phase structure corresponding to a lattice of OAM states. This phenomenon is a significant addition to the toolbox of orbital angular momentum and spin-orbit techniques that are becoming increasingly important in optical implementations of quantum information.