1. ILIAS 5-6/11/2004 WG T2 Task T2 (WG 11) AIM: exact definition (theoretical and experimental) of photo-thermal noise PARTICIPANTS INFN (AURIGA group; also LENS Florence, INOA Florence and Naple) CNRS (LKB Paris) IGR (expressed interest in the task)

2. ILIAS 5-6/11/2004 WG T2 Photo-thermal effect Physical origin: heating of mirrors by absorbed laser light  by thermal expansion: deformation/displacement due to shot noise in the absorbed radiation: displacement noise Depends on: laser power impinging on the mirrors absorption coefficient material: - thermal expansion - thermal conductivity and capacitance temperature (through the above parameters) mirror size and shape/suspension beam waist detection frequency

3. ILIAS 5-6/11/2004 WG T2 Photo-thermal effect Frequency dependence (theory): Half-space approximation: - linear decay above  c = 2k/c s w 2 where k: thermal conductivity c s : volumetric thermal capacitance w: beam waist - logarithmic below  c c (Hz) Fused silicaSapphire w/2 300K1K300K1K 10mm0.00154.80.0219000 0.1mm15480002001.9·10 8 Cut-off depending on the mirror shape and suspension (heat dispersion)

4. Mirror  half space approximation Braginsky et al., Phys. Lett. A 264, 1 (1999) Cerdonio et al., Phys. Rev. D 63, 082003 (2001)  L = L 0 K(  /  c )  1/  ILIAS 5-6/11/2004 WG T2

5. M. De Rosa et al.: “Experimental measurement of photothermal effect in Fabry-Perot cavities ”, Phys. Rev. Lett. 89, 237402 (2002) Fitting curve: L 0 /P abs = 1.5·10 -4  m/mW

6. ILIAS 5-6/11/2004 WG T2 Cryogenic operation, high Finesse cavity c : 2.8 Hz 10 kHz (fused silica) 50 MHz (sapphire) L 0 /P abs : 1.5·10 -4 m/mW 0.5·10 -5 m/mW F : 40 000 1000 000 Cryogenic operation, high Finesse cavity c : 2.8 Hz 10 kHz (fused silica) 50 MHz (sapphire) L 0 /P abs : 1.5·10 -4 m/mW 0.5·10 -5 m/mW F : 40 000 1000 000

7. ILIAS 5-6/11/2004 WG T2 Work Plan a) Years 1-2: Room temperature meas. of photo-th. noise; waist dependence b) Years 2-3: Different substrates and coatings. c) Years 1-3: Test and setup of high Finesse cavities at low T d) Years 2-4: Measurements at low T

8. ILIAS 5-6/11/2004 WG T2 a) Years 1-2: Room temperature meas. of photo-th. noise; waist dependence Work performed: Optimized the measurement apparatus: - AOM for wider and faster tuning on both cavities - EOM for amplitude modulation on one single cavity Designed and built specific mounts for using short ( small waist) cavities on the present acoustically-isolated, thermally stabilized environment Next step: Check of the previous measurements, with better accuracy (fall of half-space approximation??) Independent measurement of absorption??

9. ILIAS 5-6/11/2004 WG T2 b) Years 2-3: Different substrates and coatings Depends on the availability of different mirrors (at present: fused-silica substrates and coatings by REO

10. Setup and test of high-finesse cavities Mirrors made by J.M. Mackowski Input mirror T = 20 ppm, total losses < 10 ppm Compact cavity: L = 0.2 mm Þ Cavity finesse = 230 000, input power > 3 mW Tests at cryogenic temperature in progress