  We demonstrate that two-dimensional atomic emitter arrays with subwavelength
spacing constitute topologically protected quantum optical systems where the
photon propagation is robust against large imperfections while losses
associated with free space emission are strongly suppressed. Breaking
time-reversal symmetry with a magnetic field results in gapped photonic bands
with non-trivial Chern numbers and topologically protected, long-lived edge
states. Due to the inherent nonlinearity of constituent emitters, such systems
provide a platform for exploring quantum optical analogues of interacting
topological systems.
