  Using the Born-Oppenheimer approximation, we derive an effective Hamiltonian
for an optomechanical system that leads to a nonlinear Kerr effect in the
system's vacuum. The oscillating mirror at one edge of the optomechanical
system induces a squeezing effect in the intensity spectrum of the cavity
field. A near-resonant laser field is applied at the other edge to drive the
cavity field, in order to enhance the Kerr effect. We also propose a
quantum-nondemolition-measurement setup to monitor a system with two cavities
separated by a common oscillating mirror, based on our effective Hamiltonian
approach.

Quantum Physics