  The addition of nonlinearity to an harmonic resonator provides a route to
complex dynamical behaviour of resonant modes, including coupling between them.
We present a superconducting device that makes use of the nonlinearity of
Josephson junctions to introduce a controlled, tunable, nonlinear inductance to
a thin film coplanar waveguide resonator. Considering the device as a potential
quantum optical component in the microwave regime, we create a sensitive
bifurcation amplifier and then demonstrate spectroscopy of other resonant modes
via the intermode coupling. We find that the sensitivity of the device
approaches within a factor two quantitative agreement with a quantum model by
Dykman, but is limited by a noise that has its source(s) on-chip.
