Time reversal in matter-wave optics

. The evolution of atomic wave packets experiencing so-called comoving potential pulses is examined theoretically, in the framework of the stationary-phase approximation. The negative refraction induced by this potential is a characteristic property of negative-index media, the atomic counterpart of negative-index materials of light optics. A novel process, specific of negative-index for matter waves, is evidenced, namely a narrowing of the wave packet transiently counterbalancing the natural spreading. This is the manifestation of a general property of negative-index media, i.e. a time reversal effect. It is shown that, for a statistical ensemble of wave packets leading to a moderate dispersion of the times of flight, this time reversal phenomenon should be observable.