Approaching the quantum limit with optically instrumented multimode gravitational-wave bar detectors

A laser-illuminated Fabry-Perot cavity with a finesse of 83000 and power dissipation of a few $\mu W$ is tested at room temperature. The sensitivity to changes in the length of the cavity is 5.6×${10}^{-17\mathrm{}}$ m/√Hz. The sensitivity of multimode gravitational-wave bar detectors operated between 0.03 and 4.2 K and instrumented with a Fabry-Perot transducer of similar characteristics is calculated. The sensitivity projected for a three-mode 2400-kg Al 5056 antenna operating at 800 Hz and cooled to 0.03 K is $\delta h=6.8\mathrm{}\times {10}^{-21\mathrm{}}$ and the noise temperature of the system is a factor of 16 above the standard quantum limit. Such a sensitivity would permit observations of astrophysical significance.