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山元　一広 東京大学　宇宙線研究所　重力波推進室

鏡の熱雑音 （重力波検出器と周波数安定化）. 山元　一広 東京大学　宇宙線研究所　重力波推進室. 2011/6/24 @ 情報通信研究機構、東京. 0.Abstract. 精密測定の 原理的な限界 の一つである 鏡の熱雑音 について 　　（１） 重力波 検出器 　　（２） Cavity を用いた 周波数安定化 という２つの分野にしぼって解説します。. Contents. 1. Gravitational wave detection 2. Frequency stabilization 3. Summary.

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山元　一広 東京大学　宇宙線研究所　重力波推進室

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  1. 鏡の熱雑音 （重力波検出器と周波数安定化） 山元　一広 東京大学　宇宙線研究所　重力波推進室 2011/6/24 @情報通信研究機構、東京

  2. 0.Abstract 精密測定の原理的な限界の一つである 鏡の熱雑音について 　　（１）重力波検出器 　　（２）Cavityを用いた周波数安定化 という２つの分野にしぼって解説します。

  3. Contents 1. Gravitational wavedetection 2. Frequency stabilization 3. Summary

  4. 1.Gravitational wavedetection What is the gravitational wave ? 1915 A. Einstein : General theory of Relativity “Gravitation is curvature of space-time.” 1916 A. Einstein : Prediction of gravitational wave “Gravitational wave is ripple of space-time.” A. Einstein, S. B. Preuss. Akad. Wiss. (1916) 688. Wikipedia (A. Einstein, English)

  5. 1.Gravitational wavedetection Gravitational wave Speed is the same as that of light. Transverse wave and two polarizations http://spacefiles.blogspot.com

  6. 1.Gravitational wavedetection Interaction of gravitational wave is too weak ! Artificial generation is impossible ! Noexperiment which corresponds to Hertz experiment for electromagnetic wave Astronomical events Strain [(Change of length)/(Length)] : h ~ 10-21 (Hydrogen atom)/(Distance between Sun and Earth) No direct detection until now

  7. 1.Gravitational wavedetection Indirect detection of gravitational wave Binary pulsar (R.A. Hulse and J.H. Taylor, Astrophysical Journal 195 (1975) L51.) Generation of gravitational wave Energy emission Change of period of binary Observed change of period agrees with theoretical prediction by radiation formula of gravitational wave. J.H. Taylor et al., Nature 277 (1979) 437.

  8. 1.Gravitational wavedetection Recent result J.M. Weisberg and J.H. Taylor, ASP Conference Series, 328 (2005) 25 (arXiv:astro-ph/0407149). 8

  9. 1.Gravitational wavedetection Web site of Nobel foundation

  10. 1.Gravitational wavedetection No direct detection until now What is the motivation ? Physics : Experimental tests for theory of gravitation Astronomy : New window for astronomical observation Gravitational wave astronomy

  11. 1.Gravitational wavedetection • Gravitational wave astronomy: Burst source : Supernova Mechanism of the core-collapse SNe still unclear Shock Revival mechanism(s) after the core bounce. GWs generated by a SNe should bring information from the inner massive part of the process and could constrains on the core-collapse mechanisms. M. Punturo, GWDAW Rome 2010

  12. 1.Gravitational wavedetection Gravitational wave astronomy: Burst source : Compact binary coalescence Neutron star, Black hole quasi-mode oscillation coalescence chirp signal -300Hz -1kHz K. Kuroda Fujihara seminar (2009) msec New standard candle for measurement of distance Equation of state at high density, formation black hole

  13. 1.Gravitational wavedetection There are a lot of kinds of detectors ! Resonant detector Interferometer (on Earth) Interferometer (Space) Doppler tracking Pulsar timing Polarization of cosmic microwave background and so on … Frequency range : 10-18 Hz – 108 Hz

  14. 1.Gravitational wavedetection Interferometer (on Earth) Gravitational wave changes length difference of two arms. Frequency : 10 Hz – 10 kHz

  15. 1.Gravitational wavedetection All current interferometers have Fabry-Perot cavities.

  16. World wide network for GW astronomy GEO600 GEO HF LIGO(I) Hanford LCGT Adv. LIGO (under construction since 2008） TAMA/CLIO LCGT, Budget request Virgo Adv. Virgo (design) LIGO(I) Livingston AIGO (budget request) ET (planed) A network of detectors is indispensable to position the source. By K. Kuroda (2009 May Fujihara seminar)

  17. 1.Gravitational wavedetection LIGO (U.S.A.) 4 km, Hanford and Livingston (3000 km distance) (U.S.A.) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 17

  18. 1.Gravitational wavedetection VIRGO (Italy and France) 3 km, Pisa (Italy) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 18

  19. 1.Gravitational wavedetection GEO (Germany and U.K.) 600 m, Hannover (Germany) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 19

  20. 1.Gravitational wavedetection TAMA (Japan) 300 m, Tokyo (Japan) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.

  21. 1.Gravitational wavedetection CLIO (Japan) 100 m, Kamioka (Japan) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.

  22. 1.Gravitational wavedetection First generation (Current) LIGO (U.S.A.), VIRGO (Italy and France), GEO (Germany and U.K.), TAMA (Japan), CLIO (Japan) Second generation (Future) Advanced LIGO, Advanced VIRGO, GEO-HF, AIGO(Australia), LCGT (Japan) Third generation (Future) Einstein Telescope (Europe)

  23. 1.Gravitational wavedetection Sensitivity of interferometer 1st generation (LIGO,VIRGO) 10 times 2nd generation 10 times 3rd generation

  24. 1.Gravitational wavedetection Second generation Observation : 2017 ? – We can expect first detection ! Advanced LIGO, Advanced VIRGO, GEO-HF Upgrade of LIGO, VIRGO, and GEO AIGO (Australia)[Budget is requested.] Similar to Advanced LIGO LCGT (Japan) Cryogenic technique (Mirror temperature is 20K, small thermal motion) Underground site (small seismic motion)

  25. 1.Gravitational wavedetection Third generation Observation : 2026 ? – Einstein Telescope (Europe) 30 km vacuum tube in total Cryogenic technique Underground site (small seismic motion)

  26. Location of LCGT 3 km, Kamioka (Japan) LCGT is planed to be built underground at Kamioka, where the prototype CLIO detector is placed. By K. Kuroda (2009 May Fujihara seminar)

  27. 1.Gravitational wavedetection 最近のLCGTの進展(http://gwcenter.icrr.u-tokyo.ac.jp/) 2010年6月：文部科学省「最先端研究基盤事業」の一つとして「大型低温重力波望遠鏡の整備」が承認。 2011年3月：トンネル掘削予算承認（国会）。 2011年6月：LCGTの愛称決定(630件の応募)。 2011年7 or 8月：LCGTの愛称公表。

  28. 1.Gravitational wavedetection 今後の予定 2010/10-2014/9 : iLCGT (常温干渉計の建設) 1か月程度の観測運転 2014/10-2017/3 : bLCGT(低温干渉計の建設) 2017/4- : 長期間観測運転

  29. 1.Gravitational wavedetection 「低温工学」　 2011年7月号に LCGT特集掲載予定

  30. 1.Gravitational wavedetection Interferometric gravitational wave detector Mirrors must be free and are suspended. S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.

  31. 1.Gravitational wavedetection Thermal noise of suspension and mirror

  32. 1.Gravitational wavedetection Fluctuation-Dissipation Theorem Relation between thermal noise and mechanical loss in suspension and mirror Amplitude of thermal noise is proportional to (T/Q)1/2. In general, Q(inverse number of magnitude of Dissipation,f) depends on T(temperature).

  33. 1.Gravitational wavedetection Mirror thermal noise Two kinds of mechanical dissipation Thermoelastic damping Inhomogeneous strain Temperature gradient (via thermal expansion) Heat flow Dissipation Structure damping Unknown mechanism Almost no frequency dependence

  34. 1.Gravitational wavedetection Mirror consists of not only substrate, but also reflective coating ! Thermoelastic damping Heat flow in substrate : Substrate thermoelastic noise Heat flow between substrate and coating : Thermo-optic noise Structure damping Structure damping in substrate : Substrate Brownian noise Structure damping in coating : Coating Brownian noise 34

  35. 1.Gravitational wavedetection Temperature dependence of mirror thermal noise in LCGT Below 20 K : Thermal noise is sufficiently small for LCGT. 35

  36. 2.Frequency stabilization Thermal noise is fundamental noise of gravitational wave detection. How about the other fields ? Cavity as reference for laser frequency stabilization Current best laser frequency stabilization with rigid cavity at room temperature is limited by thermal noise of mirrors. K. Numata et al., Physical Review Letters 93 (2004) 250602.

  37. 2.Frequency stabilization Hot paper (ISI Web of Knowledge) 1 paper every 3 weeks ! (until 18 June 2011)

  38. 2.Frequency stabilization 0.1Hz/rtHz*(1Hz/f)1/2 (10mHz-1Hz) Allan deviation :4*10-16(10mHz-1Hz)

  39. 2.Frequency stabilization 世界記録（Case 1, 2011年現在でもone of the best records） B.C. Young et al., Physical Review Letters 82 (1999)3799. Spacer(ULE)の散逸による熱雑音は問題にならない。 鏡(ULE)の寄与によって決まっている。 鏡をfused silicaで作ればcoatingで決まる。

  40. 2.Frequency stabilization 世界記録（2011年現在でもone of best records） B.C. Young et al., Physical Review Letters 82 (1999)3799. これを越えるためには？ (1)Cavityを長くする。 (2)ビーム径を大きくする。 　　離れた2点間の熱雑音の相関は小さいため。 但し、factor程度の低減。 (3)Coating mechanical lossを小さくする。 (4)Cryogenic technique

  41. 2.Frequency stabilization (3)Coating mechanical lossを小さくする。 Old summary of coating mechanical loss (Ta2O5/SiO2) Similar results (same order of magnitude) f is on the order of 10-4. Loss angle : 1/Q K. Yamamoto et al., Physical Review D 74 (2006) 022002. 41

  42. 2.Frequency stabilization (3)Coating mechanical lossを小さくする。 (a)TiO2 doping (Ta2O5) TiO2 ~ 20% loss半分 G. Harry et al., Classical and Quantum Gravity 24 (2007) 405.

  43. 2.Frequency stabilization (3)Coating mechanical lossを小さくする。 (b)Ta2O5/SiO2以外の材質は？ Niobia, Hafnia, Silica+Titania, Zirconia, Almina, …. Ta2O5/SiO2を大きくしのぐものはない。 f is on the order of 10-4. Amorphous silicon X. Liu and R.O. Pohl, Physical Review B 58(1998)9067. f is on the order of 10-7~ 10-5 . 波長は1100nm以上。光学的特性は？？

  44. 2.Frequency stabilization (3)Coating mechanical lossを小さくする。 (b)Ta2O5/SiO2以外の材質は？ AlxGa1-xAs (Small oscillator) f ~ 2*10-4 at 300K, 5*10-5 at 4K G.D. Cole et al., Applied Physics Letters 92 (2008) 261108. f ~ 1*10-5 at 20K G.D. Cole et al., 2010 IEEE 23rd International Conference on Micro Electro Mechanical Systems (MEMS). Pages 847 –850

  45. 2.Frequency stabilization (4)Cryogenic technique 世界記録（Case 1, 2011年現在でもone of the best records） 鏡(ULE)の寄与によって決まっている。 鏡の散逸が小さければcoatingで決まる。 　1/3倍 Coatingの散逸が温度に依存しなければ4Kまで冷却して1/10倍。 4 K : Thermal noise is 30 times smaller (Coating dominant). 45 45 45

  46. 2.Frequency stabilization (4)Cryogenic technique 4 K : Thermal noise is 30 times smaller (Coating dominant). 300 K :0.1Hz/rtHz*(1Hz/f)1/2 (10mHz-1Hz) Allan deviation :4*10-16(10mHz-1Hz) 4 K :3 mHz/rtHz*(1Hz/f)1/2 (10mHz-1Hz) Allan deviation :1*10-17(10mHz-1Hz)

  47. 2.Frequency stabilization (4)Cryogenic technique Material of mirror and spacer Structure damping (frequency independent) in substrate Fused silica can not be used. Sapphire or Silicon are good. Q value measurement T. Uchiyama et al., Physics Letters A 261 (1999) 5-11. R. Nawrodt et al., Journal of Physics: Conference Series 122 (2008) 012008. C. Schwarz et al., 2009 Proceedings of ICEC22-ICMC2008. 47

  48. 2.Frequency stabilization (4)Cryogenic technique Laser frequency stabilization with rigid cavity at 3 K Universität Konstanz S. Seel et al., Physical Review Letters 78 (1997) 4741. 48

  49. 2.Frequency stabilization (4)Cryogenic technique At 3 K 2.5*10-15 Universität Konstanz NIST Best record at room temperature 4*10-16(limited by substrate Brownian noise) B.C. Young et al., Physical Review Letters 82 (1999) 3799.

  50. 2.Frequency stabilization (4)Cryogenic technique At 4 K 1*10-15 Some progress … H. Mueller et al., Physical Review Letters 91 (2003) 020401.

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