  We explain the phenomena of electromagnetically induced transparency (EIT) of
a weak probe field and tunable Fano resonances in hybrid optomechanics. The
system of study consists of a two-level atom coupled to a single-mode field of
an optomechanical resonator with a moving mirror. We show that a single EIT
window exists in the presence of optomechanical coupling or Jaynes-Cummings
coupling, whereas two distinct double EIT windows occur when both the couplings
are simultaneously present. Furthermore, based on our analytic and numerical
work, we prove the existence of tunable fano resonances in the system. The
controlling parameters of the system, which switch from a single EIT window to
double EIT windows and are needed to tune the fano resonances, can be realized
in present-day laboratory experiments.
