Extended Range of Dipole-Dipole Interactions in Periodically Structured Photonic Media

: The interaction between quantum two-level systems is typically short range in free space and in most photonic environments. We show that diminishing momentum isosurfaces with equal frequencies can create a significantly extended range of interaction between distant quantum systems. The extended range is robust and does not rely on a specific location or orientation of the transition dipoles. A general relation between the interaction range and properties of the isosurface is described for structured photonic media. It provides a new way to mediate long-range quantum behavior.