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Physics World

Quantum carpets, carpets of light

Michael Berry, Irene Marzoli, Wolfgang P. Schleich

Published Jun 1, 2001• 248 citations
Publisher

Abstract

In 1836 Henry Fox Talbot, an inventor of photography, published the results of some experiments in optics that he had previously demonstrated at a British Association meeting in Bristol (figure 1a). “It was very curious to observe that though the grating was greatly out of the focus of the lens...the appearance of the bands was perfectly distinct and well defined...the experiments are communicated in the hope that they may prove interesting to the cultivators of optical science.”

DOI
10.1088/2058-7058/14/6/30

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In 1836 Henry Fox Talbot, an inventor of photography, published the results of some experiments in optics that he had previously demonstrated at a British Association meeting in Bristol (figure 1a). “It was very curious to observe that though the grating was greatly out of the focus of the lens...the appearance of the bands was perfectly distinct and well defined...the experiments are communicated in the hope that they may prove interesting to the cultivators of optical science.”
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.
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.
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 investigate the suppression of matter-wave Talbot interference under environmentally induced decoherence. The system is modeled as an atomic beam diffracted by a periodic grating whose transverse dynamics is described within the paraxial approximation. Environmental coupling is introduced through an effective open-system model that exponentially damps spatial coherences between diffracted components, allowing a continuous interpolation between the coherent Talbot regime and the incoherent far-field diffraction limit. In addition to the usual intensity and transverse-momentum distributions, we analyze the local probability flow associated with the diffracted matter wave. The corresponding Bohmian, or hydrodynamic, representation is used here as a diagnostic tool fully equivalent to the standard quantum description, with no additional assumptions beyond the probability current of the paraxial wave field. In the present Talbot geometry, this analysis shows how decoherence progressively suppresses the carpet structure and smooths the transverse-momentum distribution, while the flow may remain organized into channels determined by the grating periodicity. The results illustrate, in a periodic matter-wave Talbot geometry, that the loss of visible interference and the degradation of the grating-defined flow-domain organization need not occur simultaneously. In particular, flux-channel structures can persist in parameter regimes where multislit interference features have already been strongly reduced. This distinction provides a local characterization of decoherence in matter-wave Talbot interferometry and complements previous trajectory-based analyses of coherence loss in simpler interference and confined geometries.