Interacting Qubit-Photon Bound States with Superconducting Circuits: Comparison of Theory and Experiment

Qubits strongly coupled to a photonic crystal can give rise to many exotic physical scenarios, including the realization of certain quantum many-body models and single photon and multi-photon bound states which are localized around the qubits. Here, we consider two qubits connected to a superconducting, microwave photonic crystal. We demonstrate that this system allows for controllable interactions between the two qubits and observe a fourth-order two photon virtual process indicating strong coupling between the photonic crystal and qubits. In this talk, we focus on the theoretical modeling of this experimental system and compare experimental and theoretical results. By treating the photonic crystal as a one-dimensional hopping model, we find quantitative agreement with the experimental data, including two-photon results.