The quantum limit for resolution in force measurement using active interferometric optical transducer of displacement 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. Consideration of two types of active transducer having three-level atoms gain and parametric gain is given. Noises of spontaneous emission, fluctuations due to losses in mirrors and effect of radiative friction are taken into account.
Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements impose a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a back-action evading measurement technique, or else exploit cancellations of any excess noise contributions at the detector. %Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL measurement sensitivity nearly two times better than previous measurements, and with architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. By exploiting quantum correlations created by an optical spring, we measure a total sensitivity below the SQL by
2.8 dB, corresponding to a reduction in the noise power by
72±5.1 \% below the quantum limit. Through the use of a detuned optical spring, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies ranges applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the universe.