interactions can be switched off in situ. We derive the system Hamiltonian for coupled resonator and rf SQUID. The rf SQUID dwells in the vicinity of its metastable well holding a number of energy states and acts as an artificial atom. We discuss how the Josephson symmetry breaks owing to magnetic fields in the superconducting loops. We assess that the two-photon coupling strength reaches 18 MHz which can exceed the single-photon capacitive interaction in the coupler.