  In the recent years, mater-wave interferometry has attracted growing
attention due to its unique suitability for high-precision measurements and
study of fundamental aspects of quantum theory. Diffraction and interference of
matter waves can be observed not only at a spatial aperture (such as a screen
edge, slit, or grating), but also at a time-domain aperture (such as an
absorbing barrier, or "shutter", that is being periodically switched on and
off). The wave phenomenon of the latter type is commonly referred to as
"diffraction in time". Here, we introduce a versatile, exactly solvable model
of diffraction in time. It describes time-evolution of an arbitrary initial
quantum state in the presence of a time-dependent absorbing barrier, governed
by an arbitrary aperture function. Our results enable a quantitative
description of diffraction and interference patterns in a large variety of
setups, and may be used to devise new diffraction and interference experiments
with atoms and molecules.
