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arXiv:physics/9810043

Quasiperiodic Atom Optics, Focusing, and Wave packet Rephasing

J. L. Cohen, B. Dubetsky, P. R. Berman

Published Oct 23, 1998• 0 citations
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Abstract

We propose a laser field configuration which acts as a quasiperiodic atom optical diffraction grating. Analytical and computational results for the atomic center-of-mass wavefunction after the grating reveal a quasiperiodic density pattern, a semiclassical focusing effect, and a quasiperiodic self-imaging of the atomic wavefunction analogous to a Talbot effect.

DOI
10.48550/arxiv.physics/9810043

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Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations
We propose a laser field configuration which acts as a quasiperiodic atom optical diffraction grating. Analytical and computational results for the atomic center-of-mass wavefunction after the grating reveal a quasiperiodic density pattern, a semiclassical focusing effect, and a quasiperiodic self-imaging of the atomic wavefunction analogous to a Talbot effect.
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.
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.
This dissertation explores the spatial patterns that evolve dynamically in atomic clouds and beams after they interact with one or more standing wave fields, typically formed by laser beams. The main systems under study are ensembles of free atoms, but a model Bose-Einstein condensate and the harmonic oscillator are considered as well. Focused atomic patterns with features much smaller than the wave length of the light fields are possible owing to the nonlinear atom-field interaction and are emphasized. The quantitative results combine numerical simulations and analytical expressions. Computer algorithms were developed from known methods in partial differential equations to perform the numerical simulations. The analytical results relied on standard and newly contrived techniques in quantum physics. The analytical expressions were evaluated by computer in order to extract valuable quantitative information and to compare different analytical methods with one another and with the numerical simulations. The thesis is written as a self-contained piece, and as such, develops specific examples of atom-field configurations and atomic patterns of interest from a general theory of the atoms interacting with a spatially varying light field that influences the subsequent center-of-mass motion. Beyond those already published by our group and expanded upon in the thesis, significant advances are made in: the link between transient interactions in the time- and spatial-domains; an understanding of the Raman-Nath approximation, its range of validity, and its corrections; atomic focusing by pulsed adiabatic interactions between an atom and a single standing wave light field; the differences between classical and quantum free motion after periodic interactions; the distinctions between free motion after amplitude and phase gratings; harmonic oscillator ground states kicked by spatially varying pulses; and quasiperiodic echo effects. The general theoretical structure that was detailed can be applied effectively, as intended from the outset, to other problems in atom optics.
We propose a scheme to create high-contrast, periodic atom density distributions having period $\ensuremath{\lambda}/2n$ using the Talbot effect, where $\ensuremath{\lambda}$ is the wavelength of the optical fields that scatter the atoms and n is a positive integer. This filtered Talbot lens is comprised of two standing-wave optical fields. An atomic beam propagates perpendicular to the fields. The first field, which is far detuned from the atomic transition frequency, acts as an array of lenses that focuses the atoms. The second field, positioned at the atom optical focus of the first, is resonant with the atomic transition frequency and acts as an amplitude mask, leaving unperturbed only those atoms that pass through its nodes. At distances following the interaction with the second field that are equal to an integral fraction of the Talbot length, atomic density gratings having period $\ensuremath{\lambda}/2n$ are formed.
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.