Circuit quantum electrodynamics (circuit QED) has become one of the main platforms for quantum simulation and computation. One of its notable advantages is its ability to facilitate the study of new regimes of light-matter interactions. This is achieved due to the native strong coupling between superconducting qubits and microwave resonators, and the ability to lithographically define a large variety of resonant microwave structures, for example, photonic crystals. Such geometries allow the implementation of novel forms of photon-mediated qubit-qubit interaction, cross-Kerr qubit-mediated interactions, and studies of many-body physics. In this dissertation, I will show how coplanar waveguide (CPW) lattices can be used to create engineered photon-mediated interactions between superconducting qubits. I will discuss the design and fabrication of a quasi one-dimensional lattice of CPW resonators with unconventional bands, such as gapped and ungapped flat bands. I will then present experimental data characterizing photon-mediated interactions between tunable transmon qubits and qubit-mediated non-linear photon-photon interactions in the said lattice. Our results indicate the realization of unconventional qubit-qubit interactions, therefore, demonstrating the utility of this platform for probing novel interactions between qubits and photons. In future design iterations, one can extend the study of these interactions to two-dimensional flat and hyperbolic lattices.

Pizza and drinks will be served after the seminar in ATL 2117.