Engineered circuit QED with dense resonant modes

Meta-materials are systems engineered at a wavelength smaller than the radiation considered but larger than the atomic scale; they gain their properties from their structure. Of notable interest are left-handed meta-materials. They exhibit negative permittivity and permeability. On chip quantum optics routinely use right-handed transmission lines, made of a microwave strip-line, as information mediators. In this work, we discuss the properties of a left-handed/right-handed hybrid transmission line. The resulting mode structure presents a mode pile-up at a lower cut-off frequency. Placing a qubit near the hybrid line results in strong to ultra-strong coupling to a quasi-continuum of modes. This system generates strongly entangled multi-mode states and also serves as quantum simulator for a spin-boson model with a sub-sub-ohmic density of states.