Quantum variational measurement and the "optical lever" intracavity topology of gravitational-wave detectors

The intracavity topologies of laser gravitational-wave detectors are the promising way to obtain sensitivity of these devices significantly better than the Standard Quantum Limit (SQL). The most challenging element of the intracavity topologies is the \emph{local meter} which has to monitor position of a small ($1\div10$ gram) local mirror and which precision defines the sensitivity of the detector. To overcome the SQL, the quantum variational measurement can be used in the local meter. In this method a frequency-dependent correlation between the meter back-action noise and measurement noise is introduced, which allows to eliminate the back-action noise component from the meter output signal. This correlation is created by means of an additional filter cavity. In this article the sensitivity limitations of this scheme imposed by the optical losses both in the local meter itself and in the filter cavity are estimated. It is shown that the main sensitivity limitation stems from the filter cavity losses. In order to overcome it, it is necessary to increase the filter cavity length. In a preliminary prototype experiment about 10 meter long filter cavity can be used to obtain sensitivity approximately $2\div3$ times better than the SQL. For future QND gravitational-wave detectors with sensitivity about ten times better than the SQL, the filter cavity length should be within kilometer range.