Atomic Rainbow Caustics: The Application of Catastrophe Theory to Atom Optics

by Duncan O'Dell, University of Sussex.

I will discuss the diffraction and natural focusing of atomic matter waves by an optical lattice. The de Broglie wavelength of atoms is typically rather small and so this is a good system to explore the semi-classical limit of quantum mechanics, which is non-analytic in h (unlike other famous limits in physics, such as the non-relativistic limit, which is generally smooth as v/c -> 0). We shall see that there is an emergent skeleton of singular structures, known as caustics, which dominate the diffraction pattern in the classical limit. Caustics may already be familiar to you as the bright lines on the bottom of a swimming pool or the cusp-like reflection you sometimes see in a coffee cup: caustics are the singularities of the ray theory of light. I will briefly introduce catastrophe theory as the natural language to understand this common phenomenon and demonstrate that the diffraction of atoms by optical lattices is essentially the same physics as in a rainbow.