Schematic of a possible realization of the quantum-optical Josephson interferometer with transmission line resonators in circuit QED. Here only the central conductors of the resonators are drawn. The three-resonator chip allows for a coupling J between two neighboring resonators . A voltage-node in the center is the reason for an off-center implementation of the nonlinearity U that is capacitively coupled to the middle resonator. The two outer transmission line resonators are driven by coherent input sources with amplitudes Ω. Each transmission line resonator has an individual dissipation-rate, which depends on the resonator’s coupling capacitors at both ends. We consider the case where the combined decay rate of the central resonator and the transmon is equal to the decay rate of the two outer resonators γ.