| 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. |
