Towards ultrastrong coupling of superconducting transmission line resonators

Coupled superconducting transmission line resonators have potential applications in quantum information processing and fundamental quantum mechanics. Experimentally, high coupling strengths are desirable for a clear demonstration of quantum effects. We achieve coupling strengths of 10\% of the resonator frequency (ultrastrong coupling) by distributed coupling. We find that, differently from the case of point-like coupling, the normal modes are no longer arranged symmetrically with respect to the single resonator frequency. Nevertheless, a detailed theoretical analysis shows that the system can still be described by a beam splitter Hamiltonian for two effective resonators. We expect that this result will allow for straightforward experimental access to exciting effects such as thermal entanglement in our samples.