  The control of slow and fast light propagation, in the probe transmission in
a single experiment, is a challenging task. This type of control can only be
achieved through highly nonlinear interactions and additional interfering
pathway(s), which is therefore seldom reported. Here, we devise a scheme in
which slow light, and a tunable switch from slow light to fast light can be
achieved in the probe transmission based on a hybrid setup, which is composed
of an optical cavity with two charged nano mechanical resonators (MRs). The two
MRs are electrostatically coupled via tunable Coulomb coupling strength
($g_{c}$) making a quantum opto-electromechanical system (QOEMS). The parameter
$g_{c}$ that couples the two MRs can be switched on and off by controlling the
bias voltages on the MRs, and acts as a tunable switch that allows the
propagation of transmitted probe field as slow light ($g_{c} \neq 0$) or fast
light ($g_{c} = 0$). In our scheme, the magnitude of delay and pulse
advancement can be controlled by tuning the Coulomb interaction and power of
the pump field. Furthermore, we show that slow light regime in our model is
astonishingly robust to the cavity decay rate. In comparison with previous
schemes, our scheme has clear advantages that empowers the state-of-the-art
photonic industry as well as reflects the strength of emerging hybrid
technologies.
