山元　一広東京大学　宇宙線研究所　重力波推進室

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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）

2011/6/24 @ 情報通信研究機構、東京

0.Abstract

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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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1. Gravitational wave detection 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.”

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Wikipedia (A. Einstein, English)

A. Einstein, S. B. Preuss. Akad. Wiss. (1916) 688.

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http://spacefiles.blogspot.com

Gravitational wave

Speed is the same as that of light.

Transverse wave and two polarizations


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Interaction of gravitational wave is too weak !

Artificial generation is impossible !

No experiment 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


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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.


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Recent result

J.M. Weisberg and J.H. Taylor, ASP Conference Series, 328 (2005) 25 (arXiv:astro-ph/0407149).


9Web site of Nobel foundation


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What is the motivation ?

Physics : Experimental tests for theory of gravitation

Astronomy : New window for astronomical observation

Gravitational wave astronomy

No direct detection until now


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Gravitational wave astronomy: Burst source : SupernovaMechanism 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


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Gravitational wave astronomy: Burst source

: Compact binary coalescence Neutron star, Black hole

msec

chirp signalcoalescence

quasi-modeoscillation

-300Hz -1kHz

K. Kuroda Fujihara seminar (2009)

New standard candle for measurement of distance

Equation of state at high density, formation black hole


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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


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Interferometer (on Earth)Gravitational wave changes length difference of two arms.

Frequency : 10 Hz – 10 kHz


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All current interferometers have Fabry-Perot cavities.


World wide network for GW astronomy

Adv. LIGO (under construction since 2008 ）TAMA/CLIO

LCGT, Budget request

LIGO(I) Hanford

LIGO(I) Livingston

GEO 600

Virgo

AIGO (budget request)

Adv. Virgo (design)

ET (planed)

A network of detectors is indispensable to position the source.

LCGT

By K. Kuroda (2009 May Fujihara seminar)

GEO HF

1717

LIGO (U.S.A.)

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


1818

VIRGO (Italy and France)

3 km, Pisa (Italy) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.


1919

GEO (Germany and U.K.)

600 m, Hannover (Germany) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.


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TAMA (Japan)

300 m, Tokyo (Japan) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.


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100 m, Kamioka (Japan) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.

CLIO (Japan)


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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)


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Sensitivity of interferometer

1st generation (LIGO,VIRGO)

2nd generation

3rd generation

10 times

10 times


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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)


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Einstein Telescope (Europe)

30 km vacuum tube in total

Cryogenic technique Underground site (small seismic motion)

Third generation Observation : 2026 ? –


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Location of LCGTLCGT is planed to be built underground at Kamioka, where the prototype CLIO detector is placed.

By K. Kuroda (2009 May Fujihara seminar)

3 km, Kamioka (Japan)

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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。


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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


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「低温工学」　2011 年 7 月号にLCGT 特集掲載予定


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Interferometric gravitational wave detector

Mirrors must be free and are suspended.

S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.


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Thermal noise of suspension and mirror


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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,) depends on T (temperature).


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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


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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


3535

Temperature dependence of mirror thermal noise in LCGT

Below 20 K : Thermal noise is sufficiently small for LCGT.


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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.


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Hot paper (ISI Web of Knowledge)

1 paper every 3 weeks ! (until 18 June 2011)


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

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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。


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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


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(3)Coating mechanical loss を小さくする。

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Old summary of coating mechanical loss (Ta2O5/SiO2)

Loss angle : 1/Q

Similar results (same order of magnitude)

K. Yamamoto et al., Physical Review D 74 (2006) 022002.


is on the order of 10-4.

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(a)TiO2 doping (Ta2O5)

TiO2 ~ 20% loss 半分

G. Harry et al., Classical and Quantum Gravity 24 (2007) 405.


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(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。 is on the order of 10-4.

Amorphous silicon X. Liu and R.O. Pohl, Physical Review B 58(1998)9067. is on the order of 10-7~ 10-5 .

波長は 1100nm 以上。光学的特性は？？


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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)

　

G.D. Cole et al., Applied Physics Letters 92 (2008) 261108. ~ 2*10-4 at 300K, 5*10-5 at 4K

~ 1*10-5 at 20KG.D. Cole et al., 2010 IEEE 23rd International Conference on Micro Electro Mechanical Systems (MEMS). Pages 847 –850

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(4)Cryogenic technique

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4 K : Thermal noise is 30 times smaller (Coating dominant).


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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。

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300 K : 0.1Hz/rtHz*(1Hz/f)1/2 (10mHz-1Hz) Allan deviation :4*10-16 (10mHz-1Hz)



4 K : Thermal noise is 30 times smaller (Coating dominant).

4 K : 3 mHz/rtHz*(1Hz/f)1/2 (10mHz-1Hz) Allan deviation :1*10-17 (10mHz-1Hz)

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2. Frequency stabilization(4)Cryogenic technique

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Material of mirror and spacerStructure 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.

4848

Laser frequency stabilization with rigid cavity at 3 K

S. Seel et al., Physical Review Letters 78 (1997) 4741.

Universität Konstanz



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At 3 K 2.5*10-15

Universität Konstanz

NIST

Best record at room temperature4*10-16 (limited by substrate Brownian noise)B.C. Young et al., Physical Review Letters 82 (1999) 3799.



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2. Frequency stabilization(4)Cryogenic technique

At 4 K 1*10-15

H. Mueller et al., Physical Review Letters 91 (2003) 020401.

Some progress …

5151

Laser frequency stabilization with rigid cavity at cryogenic temperature should be better !Allan deviation : 1*10-17 (limited by coating Brownian noise) Experiment : 1*10-15

Development is in progress (This is not a perfect list).

Universität Konstanz, Humboldt-Universität zu Berlin,Heinrich-Heine-Universität Düsseldorf, Physikalisch-Technischen Bundesanstalt

University of Tokyo (Tsubono lab.)



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(4)Cryogenic technique Coating : dominant source Temperature dependence ?

Loss angle is almost independent of temperature.

University of Tokyo

K. Yamamoto et al., Physical Review D 74 (2006) 022002.


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53I. Martin et al., Classical and Quantum Gravity 25(2008)055005.

Peak at 20 K ?

Glasgow University


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Annealing suppresses (Ta2O5) peak.

Glasgow University


I. Martin et al., Classical and Quantum Gravity 27(2010)225020.


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Vendor ?

M. Abernathy et al., CWADW 2011 http://agenda.infn.it/getFile.py/access?contribId=56&sessionId=15&resId=2&materialId=slides&confId=3351

Tokyo:JAEGlasgow:CSIRO


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データが集積されているが混乱も増している。

　　採用した coating の mechanical loss は当事者が測定して　　おさえておくべき！

　　 LCGT 計画では再度の測定をまもなく開始する。　　 (JAE が供給しなくなったため )


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2012 年 1 月出版予定

“Optical Coatings and Thermal Noise in Precision Measurements”, ed. by Gregory Harry, Riccardo Desalvo, and Timothy Bodiya, Cambridge University Press, in press.

重力波だけでなく、レーザー周波数安定化、量子実験などの他分野からも


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目次から2. Frequency stabilization

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目次から2. Frequency stabilization

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目次から

レーザー周波数安定化について書いてます。


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3.Summary(1) 鏡の熱雑音：精密測定の限界

(2)LCGT : 日本の大型重力波検出器計画　　鏡の熱雑音を低減するために鏡を 20K まで冷却

(3)Cavity を用いたレーザー周波数安定化：世界記録は鏡の熱雑音で制限されている。

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

6262

3.Summary(4) 周波数安定化において熱雑音の壁を越えるには

(a)Coating mechanical loss を小さくする。 (i)TiO2 doped Ta2O5/SiO2 : Loss は半分程度に (ii)Ta2O5/SiO2 以外の材質は？ Amorphous silicon, AlxGa1-xAs 　　　　光学特性は？

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3.Summary(4) 周波数安定化において熱雑音の壁を越えるには

(b)Cryogenic technique　　 4 K : Thermal noise is 30 times smaller. 　　 4 K : 3 mHz/rtHz*(1Hz/f)1/2 (10mHz-1Hz) Allan deviation :1*10-17 (10mHz-1Hz) 　　鏡や spacer はサファイアもしくはシリコン。　　採用した coating の mechanical loss は　　当事者が測定しておさえておくべき！

　　まだ常温より安定度は悪い。

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ご静聴ありがとうございました。

山元 一広 東京大学 宇宙線研究所 重力波推進室

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山元　一広東京大学　宇宙線研究所　重力波推進室