  Laser cooling of mechanical degrees of freedom is one of the most significant
achievements in the field of opto-mechanics. Here, we report, for the first
time to the best of our knowledge, efficient passive optomechanical cooling of
the motion of a freestanding waveguide coupled to a whispering-gallery-mode
(WGM) resonator. The waveguide is an 8 mm long glass-fiber nanospike, which has
a fundamental flexural resonance at {\Omega}/2{\pi} = 2.5 kHz and a Q-factor of
1.2 10**5. Upon launching 250 {\mu}W laser power at an optical frequency close
to the WGM resonant frequency, we observed cooling of the nanospike resonance
from room temperature down to 1.8 K. Simultaneous cooling of the first
higher-order mechanical mode is also observed. The strong suppression of the
overall Brownian motion of the nanospike, observed as an 11.6 dB reduction in
its mean square displacement, indicates strong optomechanical stabilization of
linear coupling between the nanospike and the cavity mode. The cooling is
caused predominantly by a combination of photothermal effects and optical
forces between nanospike and WGM resonator. The results are of direct relevance
in the many applications of WGM resonators, including atom physics,
optomechanics, and sensing.
