Circuit QED implementation of the non-perturbative boundary sine-Gordon model.

Quantum impurity problems, that describe the interaction between a degree of freedom (DOF) and an environment, are at the heart of a very rich physics covering fields as diverse as quantum optics and strongly correlated matter. In this work, we use the tools of circuit QED to address a quantum impurity problem called Boundary Sine Gordon (BSG).

To do so, we wire a highly non-linear SQUID, the DOE, to a multi-mode high impedance cavity, the environment (~4000 modes). The use of a SQUID together with our engineered environment enable us to study the BSG problem from the perturbative regime to a regime where the physics involved remains poorly understood. Thanks to our setup, we could measure the renormalization of the SQUID frequency induced by the interplay between its nonlinearity and the strong interaction with its environment. In addition to this, we have also observed the dissipation induced by the SQUID in the environment modes. The dissipation is materialized by highly non-perturbative photon conversion phenomena where a photon inserted in the cavity can reach a 10% probability of decaying after one round trip. Detailed modelling explains both the dissipation and renormalization quantitatively and confirms that the physics involved is highly non-linear, many-body and quantum.