  Atomic planar arrays offer a novel emerging quantum-optical many-body system
in which light mediates strong interactions between the atoms. The regular
lattice structure provides a cooperatively enhanced light-matter coupling and
allows for increased control and harnessing of these interactions. In
subwavelength arrays, coherent scattering of incident light beams can be highly
collimated in the forward and backward direction, resembling one-dimensional
light propagation without the need for waveguides, fibers, or resonators. The
atomic planar arrays share common features with fabricated metasurfaces, formed
by thin nanostructured films that have shown great promise in manipulating and
structuring classical light. Here we describe theoretical methods commonly
employed to analyze the cooperative responses of atomic arrays and explore some
recent developments and potential future applications of planar arrays as
versatile quantum interfaces between light and matter.
