Bloch Sphere Catastrophes

Abstract: Caustics are optical phenomena which occur when a family of rays creates an envelope of divergent intensity. Here we show that caustic surfaces also appear when a real or complex field is mapped to its order parameter manifold. We study these structures in the context of spin-1/2 fields, where the order parameter manifold is the Bloch sphere. These generic structures are a manifestation of catastrophe theory and are stable with respect to perturbations. The corresponding field configurations are also stable and represent a new type of topological defect. Equations governing the conditions for their existence and unfolding are derived.