We report microwave transmission measurements of superconducting Fabry-Perotresonators (SFPR), having a superconducting nanowire placed at a supercurrentantinode. As the plasma oscillation is excited, the supercurrent is forced toflow through the nanowire. The microwave transmission of the resonator-nanowiredevice shows a nonlinear resonance behavior, significantly dependent on theamplitude of the supercurrent oscillation. We show that suchamplitude-dependent response is due to the nonlinearity of the current-phaserelationship (CPR) of the nanowire. The results are explained within anonlinear oscillator model of the Duffing oscillator, in which the nanowireacts as a purely inductive element, in the limit of low temperatures and lowamplitudes. The low quality factor sample exhibits a "crater" at the resonancepeak at higher driving power, which is due to dissipation. We observe ahysteretic bifurcation behavior of the transmission response to frequency sweepin a sample with a higher quality factor. The Duffing model is used to explainthe Duffing bistability diagram. We also propose a concept of a nanowire-basedqubit that relies on the current dependence of the kinetic inductance of asuperconducting nanowire.
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