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Physical Review A

Optical Talbot carpet with atomic density gratings obtained by standing-wave manipulation

Chen Li, Tianwei Zhou, Yueyang Zhai, Xuguang Yue, Jinggang Xiang, Shifeng Yang, Wei Xiong, Xuzong Chen

Published Mar 20, 2017• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.95.033821

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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.
We report the experimental observation of two-dimensional Talbot effect when a resonance plane wave interacts with a two-dimensional atomic density grating generated by standing wave manipulation of ultracold Bose gases. Clear self-images of the grating and sub-images with reversed phase or fractal patterns are observed. By calculating the autocorrelation functions of the images, the behavior of periodic Talbot images is studied. The Talbot effect with two-dimensional atomic density grating expands the applications of the Talbot effect in a wide variety of research fields.
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.
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.
Fractional Talbot images in the de Broglie near field of atoms diffracted by a dispersive light grating allow the measurement of the quantum state of an electromagnetic field in a cavity, in the optical domain. In particular, the photon-number statistics may be obtained, in principle, through a single experimental realization. It may be expressed as a Fourier transform of the atomic density on a plane situated at one-fourth of the Talbot distance from the light grating. The proposed measurement of the density matrix of a standing light wave using ``Talbot fingerprints'' should be feasible within the present state of the art.
We theoretically study the Talbot effect resulting from Raman-induced grating based on periodic spatial modulation of the Raman gain and dispersion in the field of a standing pump wave. Features of integer and fractional Talbot effects are demonstrated for one- and two-dimensional (1D and 2D) Raman-induced gratings. It is shown that the intensity of diffraction images can increase due to Raman amplification in the grating. Glass-shaped diffraction patterns are demonstrated for 2D gratings. It is also shown that in the vicinity of the Talbot planes there are planes in which the diffraction patterns are spatially compressed and the intensity becomes greater. The results expand the possibility of using the Talbot effect in various applications.
We propose a laser field configuration that acts as a quasiperiodic atom optical diffraction grating. Exact analytical results for the atomic center-of-mass wave function in the Fresnel region after the grating reveal a quasiperiodic density pattern, a semiclassical focusing effect, and a quasiperiodic self-imaging of the atomic wave function analogous to a Talbot effect. The high-contrast quasiperiodic pattern that forms at the focal plane survives both transverse and longitudinal velocity averaging. The quasi-Talbot effect should be observable using atoms from Bose-Einstein condensates.