Multimode circuit QED with hybrid metamaterial transmission lines

Abstract: Quantum transmission lines are a central to superconducting and hybrid quantum computing. Parallel to these developments are those of left-handed meta-materials. They have a wide variety of applications in photonics from the microwave to the visible range such as invisibility cloaks and perfect flat lenses. For classical guided microwaves, left-handed transmission lines have been proposed and studied on the macroscopic scale. We combine these ideas in presenting a left-handed/right-handed hybrid transmission line for applications in quantum optics on a chip. The resulting system allows circuit QED to reach a new regime: multi-mode ultra-strong coupling. Out of the many potential applications of this novel device, we discuss two; the preparation of multipartite entangled states and its use as a quantum simulator for the spin-boson model where a quantum phase transition is reached up to finite size-effects.