  Optomechanically-induced transparency (OMIT) and the associated slowing of
light provide the basis for storing photons in nanoscale devices. Here we study
OMIT in parity-time (PT)-symmetric microresonators with a tunable gain-to-loss
ratio. This system features a reversed, non-amplifying transparency, i.e., an
inverted-OMIT. When the gain-to-loss ratio is varied, the system exhibits a
transition from a PT-symmetric phase to a broken-PT-symmetric phase. This
PT-phase transition results in the reversal of the pump and gain dependence of
the transmission rates. Moreover, we show that by tuning the pump power at a
fixed gain-to-loss ratio, or the gain-to-loss ratio at a fixed pump power, one
can switch from slow to fast light and vice versa. These findings provide new
tools for controlling light propagation using nanofabricated phononic devices.
