Emulating quantum photon-photon interactions in waveguides by double-wire media

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 analog emulation of such systems by unveiling an analogy between the setup of waveguide quantum electrodynamics and the classical problem of an electromagnetic wave propagating in a wire metamaterial. Experimentally measuring near electromagnetic fields, we emulate the two-particle 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.