The Jaynes-Cummings model describes the coupling between photons and a single
two-level atom in a simplified representation of light-matter interactions. In
circuit QED, this modelis implemented by combining microwave resonators and
superconducting qubits on a microchip with unprecedented experimental control.
Arranging qubits and resonators in the form of a lattice realizes a new kind of
Hubbard model, the Jaynes-Cummings-Hubbard model, in which the elementary
excitations are polariton quasi-particles. Due to the genuine openness of
photonic systems, circuit QED lattices offer the possibility to study the
intricate interplay of collective behavior, strong correlations and
non-equilibrium physics. Thus, turning circuit QED into an architecture for
quantum simulation, i.e., using a well-controlled system to mimic the intricate
quantum behavior of another system too daunting for a theorist to tackle
head-on, is an exciting idea which has served as theorists‘ playground for a
while and is now also starting to catch on in experiments. This review gives a
summary of the most recent theoretical proposals and experimental efforts in
this context.
The intriguing appeal of circuits lies in their modularity and ease of
fabrication. Based on a toolbox of simple building blocks, circuits present a
powerful framework for achievingnew functionality by combining circuit
elements into larger networks. It is an open question to what degree modularity
also holds for quantum circuits — circuits made of superconducting material,
in which electric voltages and currents are governed by the laws of quantum
physics. If realizable, quantum coherence in larger circuit networks has great
potential for advances in quantum information processing including topological
protection from decoherence. Here, we present theory suitable for quantitative
modeling of such large circuits and discuss its application to the fluxonium
device. Our approach makes use of approximate symmetries exhibited by the
circuit, and enables us to obtain new predictions for the energy spectrum of
the fluxonium device which can be tested with current experimental technology.
We assess experimentally the suitability of coupled transmission line
resonators for studies of quantum phase transitions of light. We have measured
devices with low photon hoppingrates t/2pi = 0.8MHz to quantify disorder in
individual cavity frequencies. The observed disorder is consistent with small
imperfections in fabrication. We studied the dependence of the disorder on
transmission line geometry and used our results to fabricate devices with
disorder less than two parts in 10^4. The normal mode spectrum of devices with
a high photon hopping rate t/2pi = 31MHz shows little effect of disorder,
rendering resonator arrays a good backbone for the study of condensed matter
physics with photons.