Superradiant decay and dipole-dipole interaction of distant atoms in a two-way cascaded cavity QED system

We investigate a two-way cascaded cavity QED system consisting of microtoroidal resonators coupled through an optical fiber. Each microtoroidal cavity supports two counterpropagating whispering-gallery modes coupled to single atoms through their evanescent fields. We focus on a pair of atom-microtoroid systems and compute the spectrum of spontaneous emission into the fiber with one atom initially excited. Explicit results are presented for strong-coupling and bad-cavity regimes, where the latter allows the effective atom-atom interaction to be controlled through the atom-cavity coupling and detuning: the atoms exhibit either collective spontaneous emission with no dipole-dipole interaction or a (coherent) dipole-dipole interaction and independent (single-atom) emission. This capacity for switching the character of the interaction is a feature of bidirectional coupling and connects our two-way cascaded system to work on one-dimensional waveguides. Building upon our bad-cavity results, we generalize to many atom-microtoroid systems coupled through an optical fiber.