  Observation of the Fano line shapes is essential to understand properties of
the Fano resonance in different physical systems. We explore a tunable Fano
resonance by tuning the phase shift in a Mach-Zehnder interferometer (MZI)
based on a single-mode nano-optomechanical cavity. The Fano resonance is
resulted from the optomechanically induced transparency caused by a
nano-mechanical resonator and can be tuned by applying an optomechanical MZI.
By tuning the phase shift in one arm of the MZI, we can observe the
periodically varying line shapes of the Fano resonance, which represents an
elaborate manipulation of the Fano resonance in the nanoscale optomechanics.
