  We apply the strategy of the back action evading measurement of a quadrature
component of mechanical motion of a test mass to detection of a classical force
acting on the mass (Science, 209, (1980) 547) and study both classical and
quantum limitations of the technique. We are considering a resonant
displacement transducer interrogated with a dichromatic optical pump as a model
system in this study. The transducer is represented by a Fabry Perot cavity
with a totally reflecting movable end mirror the resonant force of interest
acts upon. The cavity is pumped with two coherent optical carriers equally
detuned from one of the cavity resonances. We show that the quantum back action
cannot be completely excluded from the measurement result due to the dynamic
instability of the opto-mechanical system that either limits the allowable
power of the optical pump or calls for introducing an asymmetry to the pump
configuration destroying the quantum nondemolition nature of the measurement.
