  We theoretically investigate the optical response in a hybrid quantum
optomechanical system consisting of two optically coupled micro-cavities in
which a two-level system (qubit) is embedded on a movable membrane. The qubit
can either be a defect which interacts with the mechanical oscillator via the
linear Jaynes-Cummings interaction or a superconducting charge qubit coupled
with the mechanical mode via nonlinear interaction. We find that coherent
perfect transmission (CPT), coherent perfect synthesis (CPS) and
optomechanically induced absorption (OMIA) can be generated by suitably
adjusting the system parameters. We find that the qubit and its interaction
with the mechanical oscillator emerges as a new handle to control these quantum
optical properties. The presence of the qubit results in four points where CPT
and CPS can be realized compared to the pure optomechanical case (i.e. in the
absence of qubit) where only three points are attained. This shows that the
presence of the qubit gives us more flexibility in choosing the appropriate
parameter regime where CPT and CPS can be attained and controlled. We also find
that OMIA shows three distinct peaks both in the linear and nonlinear cases. In
the absence of the qubit, OMIA is converted to optomechanically induced
transmission (OMIT). An increase in in the qubit decay rate also shows a
transition from OMIA to OMIT. Our study reveals that the optical response of
the nonlinear case is relatively rapid (more sensitive) compared to the linear
case to changes in the system parameters. This demonstrates the potential use
of this hybrid system in designing tunable all-optical-switch and photon-router
both of which forms an important element of a quantum information network.
