Schematic and operation of the parametric amplifier. (a) Circuit diagram of a transmission line resonator based parametric amplifier. The resonator is coupled with capacitance to a transmission line where input and output modes are spatially separated using a circulator. A 20 dB directional coupler between the λ/4-resonator and the circulator is used to apply the pump field required for modulating the SQUID inductance. The second port of the directional coupler can be used to interferometrically cancel out the pump tone reflected from the sample. (b) Phase of the reflected probe signal vs. drive power for two characteristic drive frequencies below (blue) and above (red) the bifurcation threshold. (c) Illustration of the nonlinear oscillator response in the quadrature plane. The blue circle represents various input fields close to the one indicated by the gray circle in (b). Due to the nonlinear response of the resonator they are transformed into output fields indicated by the red ellipse.