Abstract

I will begin by discussing a toy model for controllably transferring light between two optical cavities, which is an important step in the realization of quantum gates based on cavity quantum electrodynamics. I will then discuss our theoretical work on ultracold atoms trapped in optical cavities pumped by lasers. The atom-field non-linearity leads to bistability in the photon number, as is well known.  What is new with ultracold atoms is that can cause bistability in the atomic motion, leading to swallowtail loops in the dispersion relation and allied phenomena.