  We report microwave transmission measurements of superconducting Fabry-Perot
resonators (SFPR), having a superconducting nanowire placed at a supercurrent
antinode. As the plasma oscillation is excited, the supercurrent is forced to
flow through the nanowire. The microwave transmission of the resonator-nanowire
device shows a nonlinear resonance behavior, significantly dependent on the
amplitude of the supercurrent oscillation. We show that such
amplitude-dependent response is due to the nonlinearity of the current-phase
relationship (CPR) of the nanowire. The results are explained within a
nonlinear oscillator model of the Duffing oscillator, in which the nanowire
acts as a purely inductive element, in the limit of low temperatures and low
amplitudes. The low quality factor sample exhibits a "crater" at the resonance
peak at higher driving power, which is due to dissipation. We observe a
hysteretic bifurcation behavior of the transmission response to frequency sweep
in a sample with a higher quality factor. The Duffing model is used to explain
the Duffing bistability diagram. We also propose a concept of a nanowire-based
qubit that relies on the current dependence of the kinetic inductance of a
superconducting nanowire.
