Dynamical diffraction of atomic matter waves by crystals of light

Atoms in light crystals formed by a standing light wave are a model system to study the propagation of matter waves in periodic potentials. The encoun tered phenomena can be described by dynamical diffraction theory which has been extensively studied for x-ray, electron, and neutron scattering from s olid state crystals. In this paper we show that an atomic de Broglie wave t raversing a standing light wave allows investigation of predictions of dyna mical diffraction theory which were previously experimentally not accessibl e. We present standard diffraction efficiency characterizations for pure ab sorptive and pure refractive crystals. Additionally we were able to measure directly the total atomic wave field formed inside a refractive and on abs orptive crystal and to confirm the predicted absolute position of the atomi c wave field with respect to the lattice planes. By superposing two standin g light waves of different frequency we tailored a new kind of crystal pote ntial where Friedel's law about usual diffraction symmetries is maximally v iolated. [S1050-2947(99)02207-6].