  A pulse of matter waves may dramatically change its shape when traversing an
absorbing barrier with time-dependent transparency. Here we show that this
effect can be utilized for controlled manipulation of spatially-localized
quantum states. In particular, in the context of atom-optics experiments, we
explicitly demonstrate how the proposed approach can be used to generate
spatially shifted, split, squeezed and cooled atomic wave packets. We expect
our work to be useful in devising new interference experiments with atoms and
molecules and, more generally, to enable new ways of coherent control of matter
waves.
