ON THE QUANTUM LIMIT FOR RESOLUTION IN FORCE MEASUREMENT IN INTERFEROMETRIC OPTICAL TRANSDUCERS OF DISPLACEMENT

The quantum limit for resolution of force using a transducer of displacement with an optical Fabry-Perot resonator is proved to be less than the standard quantum limit (SQL) if one measures not the phase but a specially chosen quadrature amplitude in the output wave, squeezed by a mechanism of ponderomotive nonlinearity. Taking into account radiative friction, introduced by the transducer into the mechanical oscillator, we show that the minimal registered force is equal to F(min) congruent-to xiF(SQL) (omega(F)/omega(o))1/4, if the mirrors of the resonator are without losses (here omega(F) is the frequency of force, omega(o) is the optical frequency and xi is a constant of the unity order, achievable at optimum pump power). Losses in mirrors limit the minimal registered force by value F(min 1) congruent-to zetaF(SQL) (R/q)1/4 where R is the sum of the loss coefficients of both mirrors and q is the transmission coefficient of the input mirror, zeta is about unity. Using Fabry-Perot resonators in a Michelson interferometer with full identical arms conserves the above results but it also gives the possibility to work with small power entering the detectors (dark fringe regime). Deterioration of sensitivity caused by small nonidentity of the arms is considered.