  We consider an optical probe that interacts with an ensemble of rare earth
ions doping a materialin the shape of a cantilever. By optical spectral hole
burning, the inhomogeneously broadenedtransition in the ions is prepared to
transmit the probe field within a narrow window, but bendingof the cantilever
causes strain in the material which shifts the ion resonances. The motion of
thecantilever may thus be registered by the phase shift of the probe. By
continuously measuringthe optical field we induce a rapid reduction of the
position and momentum uncertainty of thecantilever. Doing so, the probing
extracts entropy and thus effectively cools the thermal state ofmotion towards
a known, conditional oscillatory motion with strongly reduced thermal
fluctuations.Moreover, as the optical probe provides a force on the resonator
proportional to its intensity, it ispossible to exploit the phase shift
measurements in order to create an active feedback loop, whicheliminates the
thermal fluctuations of the resonator. We describe this system theoretically,
andprovide numerical simulations which demonstrate the rapid reduction in
resonator position andmomentum uncertainty, as well as the implementation of
the active cooling protocol.
