  We investigated the quantum state of an optomechanical suspended mirror under
continuous measurement and feedback control using Wiener filtering. We focus on
the impact of the two-mode theory of suspended mirror on the quantum state,
which is described by the pendulum and rotational modes. It is derived from the
beam model coupled to the cavity light in the low-frequency regime, including
the internal friction of the beam and the finite size effect of the mirror. We
constructed a Wiener filter for the two-mode theory and predicted the quantum
state by evaluating the conditional covariance matrix using Wiener filter
analysis. The results demonstrate that multimode analysis may play an important
role in generating the quantum squeezed state. We also point out the
possibility that one-mode analysis can be a good approximation by choosing the
range of the Fourier space in the Wiener filter analysis.
