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We experimentally demonstrate first-order (fold) and second-order (cusp)catastrophes in the density of an atomic cloud reflected from an opticalbarrier in the presence of gravity, and show their corresponding universalasymptotic behavior. The cusp point enables robust, field-free refocusing of anexpanding atomic cloud with a wide velocity distribution. Specifically, thedensity attained at the cusp point in our experiment reached 65% of the peakdensity of the atoms in the trap prior to their release. We thereby addcaustics to the various phenomena with parallels in optics that can beharnessed for manipulation of cold atoms. The structural stability ofcatastrophes provides inherent robustness against variations in the system'sdynamics and initial conditions, making them suitable for manipulation of atomsunder imperfect conditions and limited controllability.

Demonstration of fold and cusp catastrophes in an atomic cloud reflected from an optical barrier in the presence of gravity