1. GWADW 2010 in Kyoto, May 19, 2010 1 Development for Observation and Reduction of Radiation Pressure Noise T. Mori, S. Ballmer, K. Agatsuma, S. Sakata, S. Reid, O. Miyakawa, A. Nishizawa, K. Numata, H. Ishizaki, A. Furusawa, S. Kawamura, N. Mio Graduate School of Frontier Science, the University of Tokyo National Observatory of Japan

2. GWADW 2010 in Kyoto, May 19, 2010 Outline 1.Objectives and scope of the experiment 2.Setup and Experiment 3.Problems and Solutions 4.Future plans, Summary 2

3. GWADW 2010 in Kyoto, May 19, 2010 1. Objectives and Scope Objectives Observe radiation pressure (RP) noise Reduce radiation pressure noise measurement of ponderomotively squeezed vacuum fluctuations at the best homodyne phase Scope Fabry-Perot cavities with tiny mirrors and high Finesse 3 Radiation pressure noise Shot noise SQL Radiation pressure noise reduced at some homodyne phase

4. GWADW 2010 in Kyoto, May 19, 2010 Ponderomotive squeezing Squeezing ponderomotively Correlating amplitude fluctuation with phase fluctuation via back action Displacement changed by back-action of laser light and vacuum fluctuations Squeezing with frequency dependence 4 Laser light and vacuum fluctuations displacement Laser light and ponderomotively squeezed vacuum

5. GWADW 2010 in Kyoto, May 19, 2010 Conceptual design Main interferometer: Fabry-Perot Michelson interferometer with tiny mirrors (20mg) and high Finesse (10000) Output light homodyne detected with local oscillator 5 Homodyne detection Fabry-Perot Michelson interferometer Tiny mirrors High finesse signal noise h : homodyne phase signal × noise

6. GWADW 2010 in Kyoto, May 19, 2010 Noise budget 6 Laser power200 mW Injected laser power120 mW Finesse10000 End mirror mass20 mg Diameter of end mirror3 mm Thickness of end mirror1.5 mm Front mirror mass14 g Reflectivity of end mirror99.999 % Reflectivity of front mirror99.94 % Optical loss50 ppm Beam waist of end mirror 340  m Mechanical loss of substrate10 -5 Mechanical loss of coating4×10 -4 Length of silica fiber1 cm Diameter of silica fiber 10  m ・ Observation of RPN; 1×10 -17 [m/rtHz]@1 kHz ・ Ponderomotive squeezing of 6 dB Observation and reduction of RP noise between 300Hz and 1kHz

7. GWADW 2010 in Kyoto, May 19, 2010 2. Setup: Small mirror and pendulum Silica fiber attached on 20mg mirror Glued with UV cured resin 7 Diameter: 3mm Silica fiber of 10  m in diameter For lower suspension thermal noise Now 20  m: due to availability 20 mg mirror with a diameter of 3mm Effective diameter ~2mm Flat mirror

8. GWADW 2010 in Kyoto, May 19, 2010 Initial setup: single Fabry-Perot cavity Fabry-Perot cavity Cavity length: 60mm, Finesse:1400 Front mirror: fixed mirror mounted on PZT End mirror: suspension by a double pendulum Middle mass (aluminium): eddy-current damped All the core optics are on one optical table Table is suspended by a double pendulum 8 End mirror Front mirror Fabry-Perot cavity

9. GWADW 2010 in Kyoto, May 19, 2010 Assembling of a pendulum Very large yaw fluctuation prevented the stable locking Damping magnet: optimized for damping the yaw motion instead of the damping for the displacement (longitudinal) motion We could lock the cavity with this configuration (hopefully higher Eddy-current damping) much less trouble with yaw-instabilities 9 uniform magnetic field (top view)

10. GWADW 2010 in Kyoto, May 19, 2010 3. Characteristics of the cavity succeeded in the stable locking UGF: ~1kHz Phase margin: ~80deg. Limited by the mechanical resonance @4.5kHz 10 Open loop transfer function Gain Phase delay

11. GWADW 2010 in Kyoto, May 19, 2010 Sensitivity Estimated from the error signal Not optimized yet Electric noise not eliminated 11 Free running laser frequency noise (in theory) Previous measurement (20080410)

12. GWADW 2010 in Kyoto, May 19, 2010 4. Problem: Yaw instability Technically: prevents the stable locking, and makes the alignment very difficult and painful Theoretically: actuated by the radiation pressure Resonant axis is changed from center of mirror because of mirror fluctuations Yaw mode fluctuation is increased by radiation pressure → angular anti-spring effect (S. Sakata et. al., PRD81, 064023(2010)) Can be actuated easily: because of single silica fiber Torque by radiation pressure is a factor of 1000 larger than restoring force (for final cavity power) Angular control system needed Now constructing 12 Incident light Front mirror End mirror

13. GWADW 2010 in Kyoto, May 19, 2010 Negative g-factor is better, but.. Another solution for the yaw instability For yaw motion: in general always stable & unstable mode If input mirror is controlled, small mirror becomes - unstable for positive g-factor - stable for negative g-factor flat mirror: always unstable If enough budget, we will try a curved one 13 g=(1-L/R1) * (1-L/R2) 0<g<1 for optical stability  L > R2

14. GWADW 2010 in Kyoto, May 19, 2010 Problem: Q –factor Q-factor: previously measured Fiber: 10  m worse than the expected value Pendulum mode : Q= 7360 @ 5 Hz Thermal noise: slightly lower than designed RP noise 1 st violin : Q=3975 @ 1567 Hz Clamping section might be problem We will measure this again, and investigate them 14

15. GWADW 2010 in Kyoto, May 19, 2010 Future plans Now installing; Laser power: 200mW -> 500mW with frequency and amplitude stabilization system Input mirror with angular control system Now preparing; accurate measurement of the value of the system; Q-factor of the torsion and pendulum mode clarify where mechanical loss comes from ->Build a FP Michelson interferometer 15

16. GWADW 2010 in Kyoto, May 19, 2010 Summary Goal: Observation and Reduction of radiation pressure noise Key point: suspended 20 mg mirror by 10  m diameter silica fiber Cavity locked stably at low power improvement on the yaw motion damping Future plan Laser power upgrade Stabilization of the light source New input mirror suspension for yaw motion control system Build a full interferometer 16

17. GWADW 2010 in Kyoto, May 19, 2010 Thank you! 17