Metamaterials for circuit QED: Quantum simulations and other applications

The ability to design periodically structured materials not present in nature provides scientists with new tools, ranging from sub-wavelength imaging to well controlled band structures for wave propagation in photonic crystals. Superconducting metamaterials have been recently proposed to manipulate the density-of-modes of transmission lines [D. J. Egger and F. K. Wilhelm, Phys. Rev. Letters {\bf 111}, 163601 (2013)]. We further build on these ideas and develop a toolbox for environment manipulation based on nano-structured, periodic, lossless, superconducting circuits. In particular we show that high density of low energy states can be achieved using a superlattice arrangement of left-handed circuit elements. Multimode, ultra-strong coupling of superconducing qubits to such engineered environments thus allow for experimental implementation of quantum simulation of interesting new phenomena as well as for complex quantum state engineering.