1. 1 Kazuhiro Yamamoto Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut) Institut fuer Gravitationsphysik, Leibniz Universitaet Hannover Coating thermal noise and cryogenic experiments 18 May 2010 Gravitational-Wave Advanced Detector Workshop @Hearton Hotel Kyoto, Kyoto, Japan Kenji Numata University of Maryland NASA Goddard Space Flight Center

2. 0.Abstract 2 Review of coating thermal noise in cryogenic experiments (1) Temperature dependence of coating thermal noise (2) Examples of cryogenic experiments Not so new topics …. Please recover your knowledge about thermal noise !

3. Contents 1. Introduction 2. Temperature dependence of mirror thermal noise 3. Examples of cryogenic experiments 4. Summary 3

4. 1.Introduction Thermal noise of mirrors : Fundamental noise of interferometric gravitational wave detector around 100 Hz 4 How do we reduce thermal noise ? One of the simplest solutions : Cooling mirrors First feasibility study T. Uchiyama et al., Physics Letters A 242 (1998) 211.

5. 5 At almost same time, there was drastic progress in research of mirror thermal noise. 1.Introduction e.g. Coating thermal noise Y. Levin, Physical Review D 57 (1998) 659. Coating thermal noise is also a problem in other fields (frequency stabilization, quantum measurement). (1)How does thermal noise depend on temperature ? (2)Examples of cryogenic experiment

6. 6 2. Temperature dependence of mirror thermal noise Amplitude of thermal noise is proportional to (T/Q) 1/2. In general, Q (inverse number of magnitude of dissipation) depends on T (temperature). We must investigate how dissipation depends on temperature in cryogenic region.

7. 7 What kinds of thermal noise must be taken into account ? (1)Substrate Brownian noise (2)Substrate thermoelastic noise (3)Coating Brownian noise (4)Thermo-optic noise 2. Temperature dependence of mirror thermal noise

8. 8 (1) Substrate Brownian noise Structure damping (frequency independent) in substrate 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. Fused silica can not be used. Sapphire or Silicon are good. 2. Temperature dependence of mirror thermal noise

9. 9 (2) Substrate thermoelastic noise Noise by temperature fluctuation in substrate via thermal expansion M. Cerdonio et al., Physical Review D 63 (2001) 082003. 2. Temperature dependence of mirror thermal noise

10. 10 (3) Coating Brownian noise (IBS Ta 2 O 5 /SiO 2 ) Structure damping (frequency independent) in coating K. Yamamoto et al., Physical Review D 74 (2006) 022002. Loss angle is almost independent of temperature. University of Tokyo 2. Temperature dependence of mirror thermal noise

11. 11 I. Martin et al., Classical and Quantum Gravity 25(2008)055005. Peak at 20 K ? (3) Coating Brownian noise Structure damping (frequency independent) in coating Glasgow University 2. Temperature dependence of mirror thermal noise

12. 12 300C 600 C 800 C 400C 800 C 600 C 800 C 600 C 800 C 600 C 800 C 400C 600 C 800 C 400C 600 C 800 C 300C 400C 600 C 800 C (3) Coating Brownian noise Structure damping (frequency independent) in coating I. Martin et al., Einstein Telescope Meeting (March 2010). Annealing suppresses (Ta 2 O 5 ) peak. Glasgow University 2. Temperature dependence of mirror thermal noise

13. 13 Coating thermal noise is the most serious problem ! Goal temperature : below 20 K (3) Coating Brownian noise Structure damping (frequency independent) in coating It is assumed that loss is independent of temperature. 2. Temperature dependence of mirror thermal noise

14. 14 (4) Thermo-optic noise Summation of coating thermoelastic and thermo-refractive noise M. Evans et al., Physical Review D 78 (2008) 102003. Temperature fluctuation in coating 14 Coating Laser beam Surface fluctuation: Thermoelastic noise Thickness fluctuation: Thermo-refractive noise Substrate V. B. Braginsky et al., Physics Letters A 271 (2000) 303. V. B. Braginsky et al., Physics Letters A 312 (2003) 244. M.M. Fejer et al., Physical Review D 70 (2004) 082003. Thermal expansion(  ) Temperature coefficient of refractive index(  ) 2. Temperature dependence of mirror thermal noise

15. 15 (4) Thermo-optic noise Thermal expansion and specific heat : Small at cryogenic temperature in general Small contribution Material properties of coating Temperature coefficient of refractive index (  ): Unknown at cryogenic temperature It is assumed that  is 10 -5 /K (pessimistic assumption). Material properties of substrate are known. Material properties of coating are not known well (at cryogenic temperature). 2. Temperature dependence of mirror thermal noise

16. 16 (4) Thermo-optic noise Thermo-optic noise is not so serious. 2. Temperature dependence of mirror thermal noise

17. 17 (1)Gravitational wave detector (2)Rigid cavity (3)Quantum measurement 3. Examples of cryogenic experiments

18. 18 (1)Gravitational wave detector CLIO : Current project (Japan) LCGT : Second generation project (Japan) ET : Third generation project (Europe) There are many talks about these projects. 3. Examples of cryogenic experiments

19. 19 CLIO group has already demonstrated reduction of mirror thermal noise (substrate thermoelastic) by cooling mirrors (T. Uchiyama’s talk on 18 May). (1)Gravitational wave detector 3. Examples of cryogenic experiments

20. 20 (2) Rigid cavity Reference for laser frequency stabilization Experimental check of Special Relativity (Modern version of Michelson-Morley or Kennedy-Thorndike experiments) 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. Frequency stabilization with rigid cavity at 4 K should be about 30 times better than that at room temperature. 3. Examples of cryogenic experiments

21. 21 (2) Rigid cavity Current best laser frequency stabilization with rigid cavity at 3 K S. Seel et al., Physical Review Letters 78 (1997) 4741. Universität Konstanz 3. Examples of cryogenic experiments

22. 22 (2) Rigid cavity Best record at room temperature 4*10 -16 (limited by substrate Brownian noise) Best record at 3 K B.C. Young et al., Physical Review Letters 82 (1999) 3799. 2.5*10 -15 Universität Konstanz NIST 3. Examples of cryogenic experiments

23. 23 (2) Rigid cavity Laser frequency stabilization with rigid cavity at cryogenic temperature should be better ! Allan deviation : 1*10 -17 (limited by coating Brownian noise) Current best record at 3 K : 2.5*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 (previous talk by Y. Aso) 3. Examples of cryogenic experiments

24. 24 (3) Quantum measurement Small mechanical oscillator on quantum ground state Cryogenic technique (~ 4K) and laser cooling (< 1 K) is necessary to reduce thermal noise. Oscillator must have small mechanical loss at low temperature. High reflectance and low absorption are also necessary. 3. Examples of cryogenic experiments

25. 25 (3) Quantum measurement Oscillator made from coating material (Ta 2 O 5 /SiO 2 ) low absorption S. Groeblacher et al., Europhysics Letters 81 (2008) 54003. Minimum energy : 10 4 times larger than ground state energy Limit : mechanical loss (  : 3*10 -4 ~ 10 -3 ) and reflectance 3. Examples of cryogenic experiments Vienna University

26. 26 (3) Quantum measurement Oscillator (Si 3 N 4 ) with reflective coating (Ta 2 O 5 /SiO 2 ) S. Groeblacher et al., Nature Physics 5 (2009) 485. (  : 3*10 -5 ) Next step : Evacuated 3 He cryocooler Minimum energy : 32 times larger than ground state energy 3. Examples of cryogenic experiments Vienna University

27. 27 4. Summary Development of cryogenic interferometric gravitational wave detector and research of coating thermal noise started on the end of 20 th century. On the end of first decade of 21 st century, (1) We know coating Brownian noise dominates thermal noise at cryogenic temperature. (2) Reduction of mirror thermal noise (substrate thermoelastic) by cooling mirrors was demonstrated (CLIO). (3) Development of cryogenic cavity for frequency stabilization is progress (30 times better). (4) Coating thermal noise at cryogenic temperature is also hot topic in quantum measurement.

28. 28 Thank you for your attention !

29. 29 M.M. Fejer et al., Physical Review D 70 (2004) 082003.

30. 30

31. 31 S. Groeblacher et al., Nature Physics 5 (2009) 485.

32. 32 R. Nawrodt et al., New Journal of Physics 9 (2007) 225. magnetron sputtering electron beam evaporation

33. 33 3. Practical consideration in cryogenic experiments A lot of details : W. Johnson’s talk on 18 May How much can temperature of mirror be ? (1)Heat load on mirror (2)Capacity of cryocooler (3)Heat conduction between mirror and cryocooler

34. 34 (1)Heat load on mirror Light absorption 300 K radiation In the case of future interferometric gravitational wave detector, heat load is about 1 W. In the case of table top Fabry-Perot cavity, heat load is less than 10 mW. 3. Practical consideration in cryogenic experiments

35. 35 (2) Capacity of cryocooler Second law of thermodynamics : Smaller capacity at lower temperature Pulse tube cryocooler : ~ 40 W at 45 K, ~ 1 W at 4 K Evacuated 3 He cryocooler : ~ 100 mW at 1.2 K, ~10 mW at 0.7 K 3 He- 4 He dilution cryocooler : ~ 1 mW at 0.3 K In the case of future interferometric gravitational wave detector, cryocooler temperature is above 4 K. In the case of table top Fabry-Perot cavity, cryocooler temperature is above 1 K. 3. Practical consideration in cryogenic experiments

36. 36 (3) Heat conduction between mirror and cryocooler Crystal (Sapphire or Silicon) Thermal conductivity : ~ 10000 W/m/K around 20 K Temperature dependence : T 3 Small mechanical dissipation Pure metal (Aluminum or Copper) Thermal conductivity : ~ 10000 W/m/K around 10 K Temperature dependence : T 1 Large mechanical dissipation 3. Practical consideration in cryogenic experiments

37. 37 (3) Heat conduction between mirror and cryocooler Mirror at 20 K : possible Temperature dependence of thermal conductivity: T 3 Below 20 K : Difficult In the case of future interferometric gravitational wave detector, mirror must be suspended by crystal fiber (because of small mechanical dissipation). 3. Practical consideration in cryogenic experiments

38. 38 Temperature fluctuation in coating causes extra vibration due to difference of material. V. B. Braginsky et al., Physics Letters A 312 (2003) 244. M.M. Fejer et al., Physical Review D 70 (2004) 082003. 2. Temperature dependence of mirror thermal noise (4) Thermo-optic noise Coating thermoelastic noise Correlation (same origin : temperature fluctuation)