  We experimentally demonstrate first-order (fold) and second-order (cusp)
catastrophes in the density of an atomic cloud reflected from an optical
barrier in the presence of gravity, and show their corresponding universal
asymptotic behavior. The cusp point enables robust, field-free refocusing of an
expanding atomic cloud with a wide velocity distribution. Specifically, the
density attained at the cusp point in our experiment reached 65% of the peak
density of the atoms in the trap prior to their release. We thereby add
caustics to the various phenomena with parallels in optics that can be
harnessed for manipulation of cold atoms. The structural stability of
catastrophes provides inherent robustness against variations in the system's
dynamics and initial conditions, making them suitable for manipulation of atoms
under imperfect conditions and limited controllability.
