  We present a theoretical study of the linear response of a driven-dissipative
hybrid optomechanical system consisting of an interacting one-dimensional
Bose-Einstein condensate (BEC) to an external time-dependent perturbation in
the framework of the generalized linear response theory. Using the equations of
motion of the open quantum system Green's function, we obtain the linear
responses of the optical and atomic modes of the hybrid system and show how the
atom-atom interaction of the BEC atoms affects the two normal resonances of the
system as well as the anti-resonance frequency at which the optical field
amplitude of the cavity becomes zero. Furthermore, an interpretation of the
anti-resonance phenomenon is presented based on the the optical spectral
density and the self-energy.

Quantum Physics