(ed.). Gravitational waves (IOP, 2001)(422s).

112 The Earth-based large interferometer Virgoa Nd-YAG, of the order of 10 −1 –10 −2 Hz/ √ Hz at 10 Hz has been obtained, forexample by the Nice-Virgo team [8]. A copy of this circuit provides the frequencystabilization for the LFF. It is already operational and has obtained a closed loopbehaviour similar to the Virgo prestabilization circuit. The technique to reducethe influence of power fluctuation is to extract signals from the Fabry–Perot withthe well known Pound–Drever–Hall, where the injected light is phase modulatedat high frequency (usually around 10 MHz, where the laser is shot noise limited).The signal is extracted in reflection, the noise is due to the shot noise, and theSNR for the cavity detuning δν is:SNR = P in8J 0 (m)J 1 (m)F(1 − A loss Fπ) 2L c δν2 √ . (9.9)ηP DC hν 0where P in represents the incident power on the cavity, A loss the total loss in thecavity during one round trip, P DC is the DC term of the power reflected fromthe cavity, √ 2ηP DC hν is the shot noise expression with η the quantum efficiencyof the photodiode, h is the Planck constant, ν 0 is the laser frequency, L is thecavity length, F is the finesse, c is the speed of light and J 0 and J 1 are Besselfunctions, functions of the modulation depth m. The LFF cavity parameters are:Finesse 3000, P 0 = 30 mW, cavity length L = 1 cm. With these parameters,the sensitivity at 10 Hz is limited by the frequency fluctuation, and a powerspectrum density of 10 −1 Hz/ √ Hz is necessary in order to reach the displacementsensitivity of 10 −18 m/ √ Hz at 10 Hz. A prototype of the SA, called R andD SA, has been assembled in Pisa, and has tested the assembly procedure anddeveloped the control loop. LFF will suspend to the R and D SA two mirrors,in a way to create a very high finesse Fabry–Perot; of whose element, one is thestandard Virgo mirror, with a mass above 20 kg, while the other [18], usuallycalled (AX), will be different. In the early phase of the experiment the auxiliarymirror will be a standard small mirror; the auxiliary mirror will be loaded withan extra mass, in order to reduce the displacement noise due to low-frequencyradiation pressure. The Fabry–Perot cavity will act as a displacement transducerand allow the measurement of the combined thermal noise of the two mirrors, andrelated suspension. Figure 9.7 shows the experimental apparatus: the R and D SAholding the two mirrors of the cavity and the table with the optical circuit, whichwill inject light into the cavity.9.4 ConclusionSeveral gravitational-wave interferometers will be operational in a few years,and a lot of effort is being concentrated in building and making them work.Expectations are great around such experiments, since they can give essentialinformation on general relativity, fundamental physics and astrophysics. TheVirgo antenna will be operational in 2–3 years from now. A large study is goingon around the SA suspension. A special prototype called R and D SA is under