  Quantum noise limits the sensitivity of precision measurement devices, such
as laser interferometer gravitational-wave observatories and axion detectors.
In the shot-noise-limited regime, these resonant detectors are subject to a
trade-off between the peak sensitivity and bandwidth. One approach to
circumvent this limitation in gravitational-wave detectors is to embed an
anomalous-dispersion optomechanical filter to broaden the bandwidth. The
original filter cavity design, however, makes the entire system unstable.
Recently, we proposed the coherent feedback between the arm cavity and the
optomechanical filter to eliminate the instability via PT-symmetry. The
original analysis based upon the Hamiltonian formalism adopted the single-mode
and resolved-sideband approximations. In this paper, we go beyond these
approximations and consider realistic parameters. We show that the main
conclusion concerning stability remains intact, with both Nyquist analysis and
a detailed time-domain simulation.
