Practical design of the optical lever intracavity topology of gravitational-wave detectors

The quantum nondemolition (QND) intracavity topologies of gravitational-wave detectors proposed several years ago allow us, in principle, to obtain sensitivity significantly better than the standard quantum limit using relatively small amount of optical pumping power. In this article we consider an improved more practical version of the optical lever intracavity scheme. It differs from the original version by the symmetry which allows to suppress influence of the input light amplitude fluctuation. In addition, it provides the means to inject optical pumping inside the scheme without increase of optical losses. We consider also sensitivity limitations imposed by the local meter which is the key element of the intracavity topologies. Two variants of the local meter are analyzed, which are based on the spectral variation measurement and on the discrete sampling variation measurement, correspondingly. The former one, while can not be considered as a candidate for a practical implementation, allows, in principle, to obtain the best sensitivity and thus can be considered as an ideal “asymptotic case” for all other schemes. The DSVM-based local meter can be considered as a realistic scheme but its sensitivity, unfortunately, is by far not so good just due to a couple of peculiar numeric factors specific for this scheme. From our point of view search of new methods of mechanical QND measurements probably based on improved DSVM scheme or which combine the local meter with the pondermotive squeezing technique, is necessary.

Figure 1

The “optical bars” (left) and “optical lever” (right) intracavity schemes.

Figure 2

(a): Sensitivity which can be obtained in the standard extracavity topology for the coherent pumping; (b): the same for the 10 dB squeezed pumping; (c): 20 dB squeezed pumping. The left more steep parts of curves (a)–(c) correspond to Eq. (7) with $\gamma =\Omega$, the right more flat ones—to Eq. (20). (d): Potential sensitivity of the intracavity optical lever topology; (e) sensitivity of the optical lever scheme with the spectral variation measurement-based local meter; (f) sensitivity of the optical lever scheme with the DSVM-based local meter.

Figure 3

Practical design of the optical lever intracavity scheme.

Figure 4

Possible design of local meter.

Figure 5

3D plot of function $\mathcal{G}({\Omega }_B\tau ,{\Omega }_0\tau )$.

Figure 6

The scheme.