  The quality factor of a mechanical resonator is an important figure of merit
for various sensing applications and for observing quantum behavior. Here, we
demonstrate a technique to push the quality factor of a micro-mechanical
resonator beyond conventional material and fabrication limits by using an
optical field to stiffen or "trap" a particular motional mode. Optical forces
increase the oscillation frequency by storing most of the mechanical energy in
a lossless optical potential, thereby strongly diluting the effect of material
dissipation. By using a 130 nm thick SiO$_2$ disk as a suspended pendulum, we
achieve an increase in the pendulum center-of-mass frequency from 6.2 kHz to
145 kHz. The corresponding quality factor increases 50-fold from its intrinsic
value to a final value of $Q=5.8(1.1)\times 10^5$, representing more than an
order of magnitude improvement over the conventional limits of SiO$_2$ for this
geometry. Our technique may enable new opportunities for mechanical sensing and
facilitate observations of quantum behavior in this class of mechanical
systems.
