Multimode Circuit Quantum Electrodynamics with Hybrid Metamaterial Transmission Lines

Quantum transmission lines are central to superconducting and hybrid quantum computing. In this work we show how coupling them to a left-handed transmission line allows circuit QED to reach a new regime: multimode ultrastrong coupling. Out of the many potential applications of this novel device, we discuss the preparation of multipartite entangled states and the simulation of the spin-boson model where a quantum phase transition is reached up to finite size effects.