  Optical cavities with small mode volume are well-suited to detect the
vibration of sub-wavelength sized objects. Here we employ a fiber-based,
high-finesse optical microcavity to detect the Brownian motion of a freely
suspended carbon nanotube at room temperature under vacuum. The optical
detection resolves deflections of the oscillating tube down to 50pm/Hz^1/2. A
full vibrational spectrum of the carbon nanotube is obtained and confirmed by
characterization of the same device in a scanning electron microscope. Our work
successfully extends the principles of high-sensitivity optomechanical
detection to molecular scale nanomechanical systems.
