  The dominant hurdle to the operation of optomechanical systems in the quantum
regime is the coupling of the vibrating element to a thermal reservoir via
mechanical supports. Here we propose a scheme that uses an optical spring to
replace the mechanical support. We show that the resolved-sideband regime of
cooling can be reached in a configuration using a high-reflectivity disk mirror
held by an optical tweezer as one of the end-mirrors of a Fabry-Perot cavity.
We find a final phonon occupation number of the trapped mirror ${\bar n}$= 0.14
for reasonable parameters, well within the quantum regime. This demonstrates
the promise of dielectric disks attached to optical springs for the observation
of quantum effects in macroscopic objects.
