Atom induced cavities and tunable long-range interactions between atoms trapped near photonic crystals

Achieving tunable and coherent long-range interactions between cold atoms is an outstanding challenge. We propose a solution based on the powerful new platform of cold atoms trapped near nano-photonic systems. We show that atoms trapped near photonic crystals act as dielectric elements that seed localized cavity modes around the atomic position. This enables a dynamic form of “all-atomic” cavity QED, in which the mode volume and detuning of the effective cavity modes can be tuned, and atoms separated by the order of the effective cavity length can interact coherently in a manner analogous to conventional cavity QED. Considering realistic conditions such as fabrication disorder and photon losses, we find that coherent long-range potentials or spin interactions can be dominant in the system over length scales up to hundreds of wavelengths.