  Cavity optomechanics has proven to be a field of research rich with
possibilities for studying motional cooling, squeezing, quantum entanglement
and metrology in solid state systems. While to date most studies have focused
on the modulation of the cavity frequency by the moving element, the emergence
of new materials will soon allow to explore the influences of nonlinear optical
effects. We therefore study in this work the effects due to a nonlinear
position-modulated self-Kerr interaction and find that this leads to an
effective coupling that scales with the square of the photon number, meaning
that significant effects appear even for very small nonlinearities. This strong
effective coupling can lead to lower powers required for motional cooling and
the appearance of multi-stability in certain regimes.

Quantum Physics