Emulating interacting waveguide quantum electrodynamics with wire metamaterials

Abstract Arrays of atoms coupled to photons, propagating in a waveguide, are now actively studied due to their prospects for generation and detection of quantum light. Quantum simulators based on waveguides with long-range couplings were also predicted to manifest unusual many-body quantum states. However, quantum tomography for large arrays with N > 20 atoms remains elusive since it requires independent access to every atom. Here, we present a novel concept for analogue quantum simulations by mapping the setup of waveguide quantum electrodynamics to the classical problem of an electromagnetic wave, propagating in a wire metamaterial. By experimentally measuring the near electromagnetic field we emulate the localization arising from polariton-polariton interactions in the quantum problem. Our results demonstrate the potential of wire metamaterials to visualize quantum light-matter coupling in a table-top experiment and may be applied to emulate other exotic quantum effects, such as quantum chaos, and self-induced topological states.