Colloquium : Quantum matter built from nanoscopic lattices of atoms and photons

Quantum optics has advanced tremendously over the past two decades by combining ultracold atoms with diverse optical systems. However, fundamental and technical issues place constraints that limit further advances. This Colloquium examines new paradigms for strong quantum interactions of matter and light by way of atoms and photons in nanoscopic dielectric lattices, including novel quantum phases of atoms, photons, and phonons.