How to reduce suspension thermal noise in LIGO without improving the Q of the pendulum and violin modes

Abstract

The suspension noise in interferometric gravitational wave detectors is caused by losses at the top and the bottom attachments of each suspension fibre. We use the fluctuation-dissipation theorem to argue that by careful positioning of the laser beam spot on the mirror face it is possible to reduce the contribution of the bottom attachment point to the suspension noise by several orders of magnitude. For example, for the initial and enhanced LIGO (Laser Interferometer Gravitational Wave Observatory) design parameters (i.e. mirror masses and sizes, and suspension fibres' lengths and diameters) we predict a reduction of ~100 in the `bottom' spectral density throughout the band 35 - 100 Hz of serious thermal noise. We then propose a readout scheme which suppresses the suspension noise contribution of the top attachment point. The idea is to monitor an averaged horizontal displacement of the fibre of length l; this allows one to record the contribution of the top attachment point to the suspension noise, and later subtract it from the interferometer readout. This method will allow a suppression factor in spectral density of 7.4(l/d2)(Mg/ E)1/2, where d is the fibre's diameter, E is it's Young modulus and M is the mass of the mirror. For the test mass parameters of the initial and enhanced LIGO designs this reduction factor is 132 × (l/30 cm)(0.6 mm/d)2. We offer what we think might become a practical implementation of such a readout scheme. We propose to position a thin optical waveguide close to a fused silica fibre used as the suspension fibre. The waveguide itself is at the surface of a solid fused silica slab which is attached rigidly to the last mass of the seismic isolation stack (see figure 5). The thermal motion of the suspension fibre is recorded through the phaseshift of an optical wave passed through the waveguide. A laser power of 1 mW should be sufficient to achieve the desired sensitivity.