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Physical Review A

Talbot-Lau effect for atomic de Broglie waves manipulated with light

Andrey V. Turlapov, Alexey Tonyushkin, Tycho Sleator

Published Apr 25, 2005• 64 citations
Publisher

Abstract

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 $1∕10$ of the optical wavelength, demonstrating the potential application of this technique for atom nanofabrication.

DOI
10.1103/physreva.71.043612

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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.
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.
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.
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.