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Dipole-dipole interactions ( V dd ) between closely spaced atoms and molecules are related to real photon and virtual photon exchange between them and decrease in the near field connected with the characteristic Coulombic dipole field law. The control and modification of this marked scaling with distance have become a long-standing theme in quantum engineering since dipole-dipole interactions govern Van der Waals forces, collective Lamb shifts, atom blockade effects, and Förster resonance energy transfer. We show that metamaterials can fundamentally modify these interactions despite large physical separation between interacting quantum emitters. We demonstrate a two orders of magnitude increase in the near-field resonant dipole-dipole interactions at intermediate field distances (10 times the near field) and observe the distance scaling law consistent with a super-Coulombic interaction theory curtailed only by absorption and finite size effects of the metamaterial constituents. We develop a first-principles numerical approach of many-body dipole-dipole interactions in metamaterials to confirm our theoretical predictions and experimental observations. In marked distinction to existing approaches of engineering radiative interactions, our work paves the way for controlling long-range dipole-dipole interactions using hyperbolic metamaterials and natural hyperbolic two-dimensional materials. 

A bstract Searches are performed for a low-mass dimuon resonance, X , produced in proton-proton collisions at a center-of-mass energy of 13 TeV, using a data sample corresponding to an integrated luminosity of 5.1 fb − 1 and collected with the LHCb detector. The X bosons can either decay promptly or displaced from the proton-proton collision, where in both cases the requirements placed on the event and the assumptions made about the production mechanisms are kept as minimal as possible. The searches for promptly decaying X bosons explore the mass range from near the dimuon threshold up to 60 GeV, with nonnegligible X widths considered above 20 GeV. The searches for displaced X → μ + μ − decays consider masses up to 3 GeV. None of the searches finds evidence for a signal and 90% confidence-level exclusion limits are placed on the X → μ + μ − cross sections, each with minimal model dependence. In addition, these results are used to place world-leading constraints on GeV-scale bosons in the two-Higgs-doublet and hidden-valley scenarios.