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Quantum simulators employing cold atoms are among the most promisingapproaches to tackle quantum many-body problems. Nanophotonic structures arewidely employed to engineer the bandstructure of light and are thusinvestigated as a means to tune the interactions between atoms placed in theirvicinity. A key shortcoming of this approach is that excitations can decay intofree photons, limiting the coherence of such quantum simulators. Here, weovercome this challenge by proposing to use a simple cubic three-dimensionalarray of atoms to produce an omnidirectional bandgap for light and show that itenables coherent, dissipation-free interactions between embedded impurities. Weshow explicitly that the band gaps persist for moderate lattice sizes andfinite filling fraction, which makes this effect readily observable inexperiment. Our work paves the way toward analogue spin quantum simulators withlong-range interactions using ultracold atomic lattices, and is an instance ofthe emerging field of atomic quantum metamaterials.

Quantum simulation with fully coherent dipole--dipole-interactions mediated by three-dimensional subwavelength atomic arrays