Fabrication of the impedance-matched Josephson parametric amplifier and the study of the gain profile

We designed and fabricated an impedance matched Josephson junction parametric amplifier (JPA) working in the flux-pump mode for the broadband amplification of microwave signals. We developed a very simple fabrication method suitable for a small lab. We studied the phase response, as well as the gain, as a function of frequency and pump power at various pump frequencies. The phase response can be explained with the behavior of the non-linear Duffing oscillator. The observed decrease of the resonance frequency as the pump power increases, as well as the emergency of an unstable bifurcation zone, are the characteristic non-linear behavior of the Duffing oscillator. The gain profile in the stable zone can be explained with a model adapted from the theoretical model for the two-dimensional gain profile of an impedance-matched current-pumped JPA. With an appropriate environmental impedance, the theoretical model captures the features and morphology of the gain profile, such as the emergence of a gain hot zone with two branches around the resonance frequency of the JPA. Based on the gain profile, we propose that the best working zone is the merging point of the two branches of the gain hot zone before the emergence of the bifurcation zone, which gives a large bandwidth and a good gain. Over 17dB gain with a bandwidth larger than 300MHz was observed. The impedance matched JPA is used in our superconducting quantum computers for improving the fast readout fidelity of the transmon qubits.