  We present optical sideband spectroscopy measurements of a mesoscopic
mechanical oscillator cooled near its quantum ground state. The mechanical
oscillator, corresponding to a 3.99GHz acoustic mode of a patterned silicon
nanobeam, is coupled via radiation pressure to a pair of co-localized 200THz
optical modes. The mechanical mode is cooled close to its quantum ground state
from a bath temperature of 18K using radiation pressure back-action stemming
from the optical pumping of one of the optical cavity resonances. An optical
probe beam, resonant with the second optical cavity resonance, is used to
transduce the mechanical motion and determine the phonon occupancy of the
mechanical mode. Measurement of the asymmetry between up-converted and
down-converted photons of the probe beam yields directly the displacement noise
power associated with the quantum zero-point motion of the mechanical
oscillator, and provides an absolute calibration of the average phonon
occupancy of the mechanical mode.
