Quantum caustics in the dynamics of the three mode Bose-Hubbard model

Caustics are a naturally occurring wave focusing phenomenon that is well known in optics and hydrodynamics. Their significance lies in the fact that they dominate wavefields in the short wavelength limit and have universal properties including a hierarchy of characteristic shapes
described by catastrophe theory that are stable under perturbations. Here we show that the dynamics following a quench in the Bose-Hubbard trimer leads to discretized codimension-3 versions of classical wave catastrophes including the hyperbolic umbilic and elliptic umbilic catastrophes. We argue that these catastrophes are organized by the 8-dimensional corank-2 catastrophe known as X_9. These results suggest that caustics are a generic and universal feature, not just of classical waves, but also of quantum many-body wavefunctions.