Phonon pump enhanced fast and slow light in a spinning optomechanical system

We investigate the properties of the optical output fields in a spinning optomechanical system under the condition of optomechanically induced transparency (OMIT), where the cavity is optically driven by a strong pump field and a weak probe field and the mechanical resonator is driven by a coherent phonon pump. When the driven frequency of the phonon pump equals the frequency difference of the pump and probe fields, we show an enhancement OMIT, where the probe transmission can exceed unity via controlling the amplitude and phase of the phonon pump. Furthermore, the phase dispersion of the transmitted probe field is modified with manipulating the spinning direction of the resonator, which leads to a tunable delayed probe light transmission, due to the clockwise and counterclockwise optical fields in the resonator undergo the different Sagnac effect. Combining Sagnac effect, we demonstrate that the large positive or negative group delay of the output probe field can be achieved by adjusting the phase and amplitude of the coherent phonon pump, which can realize a tunable conversion between the slow and fast light effect with manipulating the spinning direction of the resonator, power of the pump field as well as the amplitude and phase of the phonon pump.