Spatially varying interactions induced in ultra-cold atoms by optical Feshbach resonance

► Optical Feshbach resonance is a key technique for generating new structures. ► Bosons can have a superfluid enclave in a Mott insulator. ► Fermions can have a normal-Fermi-gas core enclosed by a superfluid. ► We propose possible experimental setups and signatures. ► Spatially varying interactions enable cold-atoms to simulate other quantum systems.