  The harmonic oscillator is one of the most widely used model systems in
physics: an indispensable theoretical tool in a variety of fields. It is well
known that otherwise linear oscillators can attain novel and nonlinear features
through interaction with another dynamical system. We investigate such an
interacting system: a superconducting LC-circuit dispersively coupled to a
superconducting quantum interference device (SQUID). We find that the SQUID
phase behaves as a classical two-level system, whose two states correspond to
one linear and one nonlinear regime for the LC-resonator. As a result, the
circuit's response to forcing can become multistable. The strength of the
nonlinearity is tuned by the level of noise in the system, and increases with
decreasing noise. This tunable nonlinearity could potentially find application
in the field of sensitive detection, whereas increased understanding of the
classical harmonic oscillator is relevant for studies of the
quantum-to-classical crossover of Jaynes-Cummings systems.
