Coherent cavity networks with complete connectivity

When cavity photons couple to an optical fiber with a continuum of modes, they usually leak out within a finite amount of time. However, if the fiber is about one meter long and linked to a mirror, photons bounce back and forth within the fiber on a much faster time scale. As a result, {\em dynamical decoupling} prevents the cavity photons from entering the fiber. In this paper we use the simultaneous dynamical decoupling of a large number of distant cavities from the fiber modes of linear optics networks to mediate effective cavity-cavity interactions in a huge variety of configurations. Coherent cavity networks with complete connectivity can be created with potential applications in quantum computing and simulation of the complex interaction Hamiltonians of biological systems.