ON THE QUANTUM LIMIT FOR RESOLUTION IN FORCE MEASUREMENT USING AN OPTICAL DISPLACEMENT TRANSDUCER

On the example of the simplest optical transducer it is shown that in continuous coordinate measurement, back action does not limit the value of the minimum registered force if the radiative friction introduced by the device is not taken into account. It means that there is no standard quantum limit (SQL) for the resolution in the measurements of force. With radiative friction taken into account, the minimal uncertainty in force DELTAF(min) congruent-to xi DELTAF(SQL) (omega(F)/omega0)1/4 is calculated, where omega(F) is the frequency of force, omega0 is optical frequency and xi a constant of the order of unity, achievable at optimum pump power. For a mechanical resonator with intrinsic friction larger than the radiative one, the minimum error in the force measurement (at optimum pump power) is described by the quantum Nyquist formula with zero-point fluctuations energy hOMEGABAR/2 substituted by hOMEGABAR. In the reflected wave one has to measure not the phase but the quadrature amplitude in a modified homodyne scheme. It is also shown that the pump can be in a coherent state: no squeezed, photon number or any nonclassical states are required.