  We propose and experimentally demonstrate a method to prepare a nonspreading
atomic wave packet. Our technique relies on a spatially modulated absorption
constantly chiseling away from an initially broad de Broglie wave. The
resulting contraction is balanced by dispersion due to Heisenberg's uncertainty
principle. This quantum evolution results in the formation of a nonspreading
wave packet of Gaussian form with a spatially quadratic phase. Experimentally,
we confirm these predictions by observing the evolution of the momentum
distribution. Moreover, by employing interferometric techniques, we measure the
predicted quadratic phase across the wave packet. Nonspreading wave packets of
this kind also exist in two space dimensions and we can control their amplitude
and phase using optical elements.
