Due to their mixed photon-electronic excitation character, cavity polaritons have highly interesting properties. Especially interesting is the so-called ultrastrong coupling regime, reached when the strength of the photon-two-level system coupling is larger than the energy of the resonant state. We have recently demonstrated that terahertz metamaterials coupled to high-mobility two-dimensional electron gases is an almost ideal, field-tunable system that enables the exploration of this ultra-strong coupling regime.In this project, we want to explore four key physical questions opened by this new approach. First we plan to explore the limit of ultra-strong coupling in our systems, including the emission of Casimir-like squeezed vacuum photons upon non-adiabatic change in the coupling energy and parametric generation of light. Secondly we would like to test a theoretical prediction anticipating, in the ultra-strong coupling regime, a quantum phase transition to a Dicke superradiant state upon substitution of the GaAs/AlGaAs two-dimensional electron gas by a graphene layer or multilayers. Thirdly, we claim that our metamaterial-based system also enables the study of coupled polaritons by either direct meta-atom electromagnetic coupling or using a waveguide bus and superconducting circuits. Finally, we want to explore polaritonic emitters and non-linear elements.