Long-Range Interactions in Weyl-Dense Atomic Arrays Protected from Dissipation and Disorder

Long-range interactions are a key resource in many quantum phenomena and technologies. Free-space photons mediate power-law interactions but lack tunability and suffer from decoherence processes due to their omnidirectional emission. Engineered dielectrics can yield tunable and coherent interactions, but typically at the expense of making them both shorter ranged and sensitive to material disorder and photon loss. Here, we propose a platform that can circumvent all these limitations based on three-dimensional subwavelength atomic arrays subjected to magnetic fields. Our key result is to show how to design the polaritonic bands of these atomic metamaterials to feature a pair of frequency-isolated Weyl points, i.e., points in reciprocal space around which the bands disperse linearly and defining monopoles of the Berry curvature. As predicted by recent works, such Weyl excitations can mediate interactions that are simultaneously long range, due to their gapless nature; robust, due to the topological protection of Weyl points; and decoherence-free, due to their subradiant character. We demonstrate the robustness of these isolated Weyl points for a large regime of interatomic distances and magnetic field values and characterize the emergence of their corresponding Fermi arcs surface states. The latter can lead to two-dimensional, nonreciprocal atomic interactions with no analogue in other chiral quantum optical setups.