  We have studied nonlinear superconducting resonators: lambda/2
coplanar-waveguide (CPW) resonators with Josephson junctions (JJs) placed in
the middle and lambda/4 CPW resonators terminated by JJs, which can be used for
the qubit readout as "bifurcation amplifiers." The nonlinearity of the
resonators arises from the Josephson junctions, and because of the
nonlinearity, the resonators with appropriate parameters are expected to show a
hysteretic response to the frequency sweep, or "bifurcation," when they are
driven with a sufficiently large power. We designed and fabricated resonators
whose resonant frequencies were around 10 GHz. We characterized the resonators
at low temperatures, T<0.05 K, and confirmed that they indeed exhibited
hysteresis. The sizes of the hysteresis, however, are sometimes considerably
smaller than the predictions based on the loaded quality factor in the weak
drive regime. When the discrepancy appears, it is mostly explained by taking
into account the internal loss, which often increases in our resonators with
increasing drive power in the relevant power range. As a possible origin of the
power-dependent loss, the quasiparticle channel of conductance of the JJs is
discussed.
