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

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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.