Demonstration of Fold and Cusp Catastrophes in an Atomic Cloud Reflected from an Optical Barrier in the Presence of Gravity

Our manuscript describes the application of catastrophes in the field of atom optics, in which various optical phenomena such as lenses and curved mirrors have been mimicked by harnessing optical and magnetic potentials to guide ultracold atoms. Such devices are naturally suitable for ultracold atomic beams, in which the atoms have negligible longitudinal velocity spread, and accordingly can be considered analogous to an optical beam. Like optical lenses and curved mirrors, the focusing they provide is geometry-dependent.However, focusing does occur abundantly in nature in a way that is less optimal than lens-like imaging, yet much more robust. Such are the optical caustics – like the bright curves of light at the bottom of swimming pools, or the cusp feature at the bottom of an empty cup. Unlike focusing with a lens, caustics are inherently immune to changes in the parameters of the system in which they occur. This is the reason bright curves of light appear nearly always in every pool, even though the shape and dimensions of the pools may vary significantly. Their robustness makes caustics a potentially powerful tool for control under imperfect conditions or limited controllability. This was demonstrated, for example, by focusing of electron flow [Science 315, 1252 (2007)], and high-harmonics generation with atto-second pulses [Nature Photonics 6, 170–173 (2012)].

We follow this line and demonstrate the potential of adding the universal phenomenon of caustics to the toolbox of atom optics. Following singularity theory, we present the evolution of atoms in the presence of a conserving potential as a topological mapping. This mapping can result in the occurrence of catastrophes, which are classes of structurally-stable singularity points at which the density diverges. Similarly, optical caustics are classified into different types of such catastrophes.

We demonstrate the two orders of catastrophes that can appear in the linear density of an atomic cloud,which are fold lines (first order) and a cusp point (second order). The image below shows our demonstration of a cusp point in an expanding, hot atomic cloud, reflected from an ptical barrier. By attaining this point, we in fact re-focus a cloud that has ‘exploded’ 50ms earlier. This focusing is field-free, i.e. arises from the free-propagation of the atoms under gravity, far away from any perturbing fields. Such focusing in the longitudinal direction cannot be achieved with lens-like potentials or curved mirrors, as such do not distinguish between fast and slow atoms that travel along the same path. To summarize, in this work we experimentally demonstrate the universal and fundamental behavior of this atomic system, link it to many other, drastically diverse physical systems, and offer a potentially powerful experimental tool.