Development for Observation and Reduction of Radiation Pressure Noise

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. Outline Objectives and scope of the experiment Setup and Experiment Problems and Solutions Future plans, Summary

3. 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 Radiation pressure noise Radiation pressure noise reduced at some homodyne phase SQL Shot noise

4. 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 Laser light and vacuum fluctuations Laser light and ponderomotively squeezed vacuum displacement

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

6. Noise budget • Observation and reduction of RP noise between 300Hz and 1kHz ・ Observation of RPN; 1×10-17 [m/rtHz]@1 kHz ・ Ponderomotive squeezing of 6 dB

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

8. 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 Fabry-Perot cavity End mirror Front mirror

9. 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 uniform magnetic field (top view)

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

11. Sensitivity • Estimated from the error signal • Not optimized yet • Electric noise not eliminated Free running laser frequency noise (in theory) Previous measurement (20080410)

12. 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 Front mirror Incident light End mirror

13. 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 g=(1-L/R1) * (1-L/R2) • 0<g<1 for optical stability •  L > R2

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

15. 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

16. Summary • Goal: Observation and Reduction of radiation pressure noise • Key point: suspended 20 mg mirror by 10 mm 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

17. Thank you!