Selective readout and back-action reduction for wideband acoustic gravitational wave detectors

We present the concept of the “selective readout” for the recently proposed dual detector [M. Cerdonio et al., Phys. Rev. Lett. 87, 031101 (2001)] of gravitational waves which is a sensitive and broadband resonant-mass detector. The advantage of the proposed detection scheme is that it is made sensitive only to the acoustic modes of the masses forming the detector that have quadrupolar symmetry, and thus carry the signal, while it rejects efficiently the noise contribution from the other modes, either of thermal or back-action origin. The total effect is that the sensitivity of a dual detector equipped with the selective readout is flat within a wide frequency range and can be as good as $\sim 8\times {10}^{-24}/\sqrt{\mathrm{Hz}}$ between 1.3 and 4 kHz for a silicon carbide detector, 3 m in diameter.