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Optics Express

Realization of optical carpets in the Talbot and Talbot-Lau configurations

William B. Case, Mathias Tomandl, Sarayut Deachapunya, Markus Arndt

Published Nov 2, 2009• 140 citations
Publisher

Abstract

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.

DOI
10.1364/oe.17.020966

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Physical Review A•Apr 25, 2005•64 citations
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.
A well-known phenomenon in both optics and quantum mechanics is the so-called Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both N-slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the Talbot-Beeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.
We report a method of generating atomic density gratings by standing-wave manipulation of ultracold Bose gases. By illuminating the gratings with a beam of homogeneous light, we observe one- and two-dimensional Talbot carpets. We further measure the autocorrelation function of the images, which varies with image plane position caused by Talbot effect. Periodically repeated self-images and subimages of the atomic density gratings are observed clearly. Our theoretical calculations and experimental results agree well with each other. The atomic density gratings hold promise for substituting for traditional gratings in many applications.
Summary form only given.Recent developments in atom optics have led to different approaches to lithographic techniques with neutral atoms. One of these is the use of diffraction from free-standing masks, which is sometimes called atom holography. There, narrow structures arise due to matter-wave interference in the Fresnel regime. In the presented experiment, we demonstrate that the wave nature of atoms can be used to produce periodic structures with small periodicities. We used the Talbot effect in the Fresnel diffraction regime behind a microfabricated transmission grating. The Talbot effect is the self-imaging of a grating of periodicity d illuminated with plane coherent waves.
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.
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.
We have demonstrated the Talbot-Lau effect for atomic de Broglie waves in the time domain. This effect is based on Fresnel diffraction of matter waves from an incoherent source. In the experiment, de Broglie waves of atoms in a particular internal state have been manipulated and the resulting density directly imaged by resonant optical fields. These experiments allow us to probe the quantum dynamics of the atomic center of mass. We have also used this effect to create patterns in the density of the atoms with period as small as 1∕101∕101∕10 of the optical wavelength, demonstrating the potential application of this technique for atom nanofabrication.