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 sideband-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.
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