  Optomechanics allows the transduction of weak forces to optical fields, with
many efforts approaching the standard quantum limit. We consider force-sensing
using a mirror-in-the-middle setup and use two coupled cavity modes originated
from normal mode splitting for separating pump and probe fields. We find that
this two-mode model can be reduced to an effective single-mode model, if we
drive the pump mode strongly and detect the signal from the weak probe mode.
The optimal force detection sensitivity at zero frequency (DC) is calculated
and we show that one can beat the standard quantum limit by driving the cavity
close to instability. The best sensitivity achievable is limited by mechanical
thermal noise and by optical losses. We also find that the bandwidth where
optimal sensitivity is maintained is proportional to the cavity damping in the
resolved sideband regime. Finally, the squeezing spectrum of the output signal
is calculated, and it shows almost perfect squeezing at DC is possible by using
a high quality factor and low thermal phonon-number mechanical oscillator.
