  We theoretically investigate optical detection of a weak classical force
acting on a free particle in a dissipative coupling optomechanical system with
a degenerate parametric amplifier (PA). We show that the PA allows one to
achieve the force sensitivity far better than the standard quantum limit (SQL)
over a broad range of the detection frequencies. The improvement depends on the
parametric gain and the driving power. Moreover, we discuss the effects of the
mechanical damping and the thermal noise on the force sensitivity. We find that
the robustness of the force sensitivity much better than the SQL against the
mechanical damping and the thermal noise is achievable in the presence of the
PA with a high parametric gain. For the temperature $T = 1$ K, the improvement
in sensitivity is better by a factor of about 7 when the driving power is set
at a value corresponding to the SQL with no PA.
