Ultrastrong coupling dynamics with a transmon qubit

The interaction of light and matter is often described by the exchange of single excitations. When the coupling strength is a significant fraction of the system frequencies, the number of excitations are no longer preserved and that simple picture breaks down. This regime is known as the ultrastrong coupling regime and is characterized by non-trivial light-matter eigenstates and by complex dynamics. In this work, we propose to use an array Josephson junctions to increase the impedance of the light mode enabling ultrastrong coupling to a transmon qubit. We show that the resulting dynamics can be generated and probed by taking advantage of the multi-mode structure of the junction array. This proposal relies on the frequency tunability of the transmon and, crucially, on the use of a low frequency mode of the array, which allows for non-adiabatic changes of the ground state.