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 70pm/Hz1/2. 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 extends the principles of high-sensitivity optomechanical detection to molecular scale nanomechanical systems.

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