  We propose and experimentally demonstrate the generation of enhanced optical
springs using the optical Kerr effect. A nonlinear optical crystal is inserted
into a Fabry-Perot cavity with a movable mirror, and a chain of second-order
nonlinear optical effects in the phase-mismatched condition induces the Kerr
effect. The optical spring constant is enhanced by a factor of $1.6\pm0.1$ over
linear theory. To our knowledge, this is the first realization of
optomechanical coupling enhancement using a nonlinear optical effect, which has
been theoretically investigated to overcome the performance limitations of
linear optomechanical systems. The tunable nonlinearity of demonstrated system
has a wide range of potential applications, from observing gravitational waves
emitted by binary neutron star post-merger remnants to cooling macroscopic
oscillators to their quantum ground state.
