Completely subradiant multi-atom architectures through 2D photonic crystals

Inspired by recent advances in the manipulation of atoms trapped near 1D waveguides and pro- posals to use surface acoustic waves on piezoelectric substrates for the same purpose, we show the potential of two-dimensional platforms. We exploit the directional emission of atoms near photonic crystal slabs with square symmetry to build perfect subradiant states of 2 distant atoms, possible in 2D only for finite lattices with reflecting boundaries. We also show how to design massively parallel 1D arrays of atoms above a single crystal, useful for multi-port output of nonclassical light, by ex- ploiting destructive interference of guided resonance modes due to finite size effects. Directionality of the emission is shown to be present whenever a linear iso-frequency manifold is present in the dispersion relation of the crystal. Multi-atom radiance properties can be obtained from a simple cross-talk coefficient of a master equation, which we compare with exact atom-crystal dynamics, showing its predictive power.