  Parametric coupling of optical and mechanical degrees of freedom forms the
basis of many ultra-sensitive measurements of both force and mechanical
displacement. An optical cavity with a mechanically compliant boundary enhances
the optomechanical interaction, but also gives rise to qualitatively new
coupled dynamics. As early as 1967, in a pioneering work, V. Braginsky analyzed
theoretically the role of radiation pressure in the interferometric measurement
process, but it has remained experimentally unexplored for many decades. Here,
we use whispering-gallery-mode (WGM) optical microresonators to study these
radiation pressure phenomena. Optical microresonators simultaneously host
optical and mechanical modes, which are systematically analyzed and optimized
to feature ultra-low mechanical dissipation, photon storage times exceeding the
mechanical oscillation period (i.e. the "resolved-sideband regime") and large
optomechanical coupling. It is demonstrated that dynamical backaction can be
employed to cool mechanical modes, i.e., to reduce their thermally excited
random motion. Utilizing this novel technique together with cryogenic
pre-cooling of the mechanical oscillator, the phonon occupation of mechanical
radial-breathing modes could be reduced to about 60 excitation quanta. The
corresponding displacement fluctuations are monitored interferometrically with
a sensitivity at the level of 10^-18 m/Hz^(1/2), which is below the imprecision
at the standard quantum limit (SQL). It is shown that optical measurement
techniques employed here are operating in a near-ideal manner according to the
principles of quantum measurement, displaying a backaction-imprecision product
close to the quantum limit. An outlook on optomechanical experiments with
crystalline WGM resonators and the effect of "optomechanically induced
transparency" (analogous to electromagnetically induced transparency) is given.
