1. 1 Kazuhiro Yamamoto Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut) Institut fuer Gravitationsphysik, Leibniz Universitaet Hannover Fundamental noise of interferometric gravitational wave detector (Thermal noise) 7 May 2010 @Università degli Studi di Trento, Trento, Italy

2. 2 6 May 2010 (Afternoon) Gravitational wave and detectors 7 May 2010 (Morning) Fundamental noise of interferometric gravitational wave detectors

3. 3 7 May 2010 (Morning) Thermal noise 7 May 2010 (Morning) Seismic noise, Quantum noise

4. 0.Abstract 4 I would like to explain … (1) What is fundamental noise of interferometer ? (2) Basic knowledge of thermal noise (3) Drastic progress of research of thermal noise in last about 10 years

5. Contents 1. Outline of fundamental noise 2. Thermal noise before 1960 3. Thermal noise before 1995 4. Revolutions after 1995 5. Summary 5

6. 1.Outline of fundamental noise Interferometric gravitational wave detector Mirrors must be free and are suspended. 6 S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.

7. 7 http://spacefiles.blogspot.com 1.Outline of fundamental noise Typical example of sensitivity of interferometer (LCGT)

8. 8 1.Outline of fundamental noise Seismic noise Vibration of ground shakes mirrors.

9. 9 1.Outline of fundamental noise Thermal noise Mirrors and suspension are in heat bath. Limit from statistical mechanics Random energy flow from heat bath

10. 10 1.Outline of fundamental noise Quantum noise Quantum amplitude and phase fluctuations of light Limit from quantum mechanics

11. 11 2.Thermal noise before 1960 History before gravitational wave detector Robert Brown investigated random motion of small particles (~1  m) in water. R. Brown, Philosophical Magazine 4 (1828) 161. Mechanism was unknown. Many ideas were proposed and rejected. Random collisions with atoms of water ? G. Cantoni, Nuovo Ciment 27 (1867) 156. J. Delsaulx They are not proof but guesses.

12. 12 2.Thermal noise before 1960 Albert Einstein showed theory of Brownian motion. A. Einstein, Annalen der Physik 17 (1905) 549. Relation between diffusion of particles and viscosity of water Evidence of existence of atom Wikipedia (A. Einstein, English) Jean Baptiste Perrin’s experiment proved that Einstein’s theory is correct. J. Perrin, Ann. Chim. Phys. 18 (1909) 1.

13. 13 2.Thermal noise before 1960 Presentation speech of Nobel prize in Physics 1921 (Laureate is A. Einstein) Throughout the first decade of this century the so-called Brownian movement stimulated the keenest interest. In 1905 Einstein founded a kinetic theory to account for this movement by means of which he derived the chief properties of suspensions, i.e. liquids with solid particles suspended in them. This theory, based on classical mechanics, helps to explain the behaviour of what are known as colloidal solutions, a behaviour which has been studied by Svedberg, Perrin, Zsigmondy and countless other scientists within the context of what has grown into a large branch of science, colloid chemistry. Web site of Nobel foundation

14. 14 2.Thermal noise before 1960 Web site of Nobel foundation

15. 15 Thermal fluctuation of electrical voltage (or current) J.B. Johnson, Physical Review 32 (1928) 97. Measurement H. Nyquist, Physical Review 32 (1928) 110. Theory 2.Thermal noise before 1960 Relation between electrical fluctuation and resistance

16. 16 2.Thermal noise before 1960 Finally, general theorem appeared. Fluctuation-Dissipation Theorem (FDT) H.B. Callen and R.F. Greene, Physical Review 86 (1952) 702. R.F. Greene and H.B. Callen, Physical Review 88 (1952) 1387. Relation between thermal fluctuation and dissipation Fluctuation : Energy from heat bath Dissipation : Energy to heat bath Interaction between system and heat bath

17. 17 2.Thermal noise before 1960 Fluctuation-Dissipation Theorem is valid if (1)system is linear. (2)system is in thermal equilibrium. Relation between diffusion (fluctuation) of particles and viscosity (dissipation) of water Brownian motion Electric circuit Relation between electrical fluctuation and resistance (dissipation) They are only examples of FDT !

18. 18 3.Thermal noise before 1995 Basis of thermal noise of interferometric detector Thermal noise of suspension and mirror

19. 19 Resonant frequency : suspension : ~ 1 Hz mirror : > 10 kHz Target frequency of gravitational wave : ~ 100 Hz Off resonance thermal noise 3.Thermal noise before 1995 Suspension and mirror : Mechanical harmonic oscillator Residual gas damping is not a problem because interferometer in vacuum (< 10 -7 mbar). Mechanical loss in suspension and mirror is crucial.

20. 20 3.Thermal noise before 1995 Spectrum density of thermal noise of harmonic oscillator Viscous damping : Friction force is proportional to velocity. Structure damping : Loss is independent of frequency. Loss in many materials are structure damping.

21. 21 3.Thermal noise before 1995 Spectrum density of thermal noise of harmonic oscillator Q-value : Magnitude of loss Higher Q is smaller loss. Higher Q is smaller off resonance thermal noise and better.

22. 22 3.Thermal noise before 1995 Measurement of Q-value (Width of resonance peak) If Q-value is too high, measurement is difficult.

23. 23 3.Thermal noise before 1995 Measurement of Q-value (Decay time of resonance motion) In (our) usual cases, we adopt this method.

24. 24 3.Thermal noise before 1995 Recoil loss (problem in measurement of decay time) Contamination of loss in support system Suspension : Rigid and heavy support system

25. 25 3.Thermal noise before 1995 Recoil loss (problem in measurement of decay time) Mirror : Nodal support system (Center of flat surface is node for many modes) K. Numata et al., Physics Letters A 276 (2000) 37.

26. 26 3.Thermal noise before 1995 Measurement of Q-value of pendulum (monolithic fused silica) Q = 2.3 * 10 7 G. Cagnoli et al., Physical Review Letters 85 (2000) 2442.

27. 27 3.Thermal noise before 1995 K. Numata et al., Physics Letters A 327 (2004) 263. Measurement of Q-value of fused silica mirror Q = 4 * 10 7 Structure damping Not structure damping

28. 28 3.Thermal noise before 1995 Evaluated thermal noise based on Q-value measurement

29. 29 4.Revolutions after 1995 (1)Thermoelastic noise (2) Thermal noise caused by inhomogeneous loss (3) Direct measurement of thermal noise (4) Reduction of thermal noise

30. 30 4.Revolutions after 1995 (1)Thermoelastic noise Thermoelastic damping : a kind of loss Inhomogeneous strain Thermal expansion coefficient Temperature gradient Heat flow We can calculate thermoelastic noise using only material properties. Drawing by Tobias Westphal

31. 31 4.Revolutions after 1995 (1)Thermoelastic noise Thermoelastic noise : thermal noise by thermoelastic damping Other interpretation Temperature fluctuation Thermal expansion coefficient Deformation of elastic body

32. 32 4.Revolutions after 1995 (1)Thermoelastic noise Long, long history of research of thermoelastic damping 1 dimension (bar, ribbon) C. Zener, Physical Review 52 (1937) 230; 53 (1938) 90. 2 dimension (disk) L.D. Landau and E.M. Lifshitz “The Theory of Elasticity”, 1953. A.S. Nowick and B. Berry “Anelastic Relaxation in Crystalline Solids”, 1972. 3 dimension (mirror) 1999

33. 33 (1)Thermoelastic noise Thermoelastic noise of 3 dimension mirror without coating V. B. Braginsky et al., Physics Letters A 264 (1999) 1. We can calculate thermoelastic noise using only material properties. This noise is larger than expectation ! 4.Revolutions after 1995

34. 34 4.Revolutions after 1995 (1)Thermoelastic noise Fused silica vs. Sapphire Current interferometric gravitational wave detector Fused silica mirror Future interferometer Sapphire was a candidate. Optical properties of fused silica is better. It was expected that thermal noise of sapphire is smaller. However …

35. 35 4.Revolutions after 1995 One of advantages of sapphire was lost. Future (room temperature) interferometer will use fused silica mirror. (1)Thermoelastic noise

36. 36 4.Revolutions after 1995 (1)Thermoelastic noise Thermo-optic noise Temperature fluctuation in reflective coating Thermal expansion (  ) Temperature coefficient of refractive index (  ) Fluctuation of phase of reflected light Material properties of reflective coating are important issues. V. B. Braginsky et al., Physics Letters A 312 (2003) 244. V. B. Braginsky et al., Physics Letters A 271 (2000) 303. M. Evans et al., Physical Review D 78 (2008) 102003.

37. 37 4.Revolutions after 1995 (2) Thermal noise caused by inhomogeneous loss Mirror consists of not only bulk ! Reflective coating Magnet (coil-magnet actuator to control mirror position) Thickness of coating : ~ 5  m Thickness of mirror : ~ 10 cm Nobody cared. Magnets decrease Q-values. Serious problem

38. 38 (2) Thermal noise caused by inhomogeneous loss 4.Revolutions after 1995 Y. Levin, Physical Review D 57 (1998) 659. Laser beam Q-value of loss at A is the same as that at B. Loss at A can shake illuminated surface more largely owing to conservation of momentum. Thermal noise depends on not only Q-values but also spatial distribution of loss.

39. 39 4.Revolutions after 1995 (2) Thermal noise caused by inhomogeneous loss Quantitative discussion K. Yamamoto et al., Physics Letters A 305 (2002) 18. Reflective coating Magnet It can be a problem. No problem

40. 40 4.Revolutions after 1995 (2) Thermal noise caused by inhomogeneous loss Old summary of coating mechanical loss Loss angle : 1/Q Similar results (same order of magnitude) Structure damping K. Yamamoto et al., Physical Review D 74 (2006) 022002.

41. 41 4.Revolutions after 1995 (2) Thermal noise caused by inhomogeneous loss Evaluated thermal noise based on measurement Coating thermal noise is the most serious problem !

42. 42 (3) Direct measurement of thermal noise 4.Revolutions after 1995 Are formulae of thermal noise correct ? Direct measurement of thermal noise of mirror University of Tokyo, California Institute of Technology Small beam radius (about 0.1 mm) to enhance thermal noise Cavity length ~ 1 cm Direct measurement of thermal noise of suspension University of Tokyo Underground site with small seismic motion Cavity length ~ 100 m

43. 43 4.Revolutions after 1995 (3) Direct measurement of thermal noise BK7 : Structure damping in substrate K. Numata et al., Physical Review Letters 91 (2003) 260602.

44. 44 4.Revolutions after 1995 (3) Direct measurement of thermal noise Calcium fluoride : Thermoelastic damping in substrate K. Numata et al., Physical Review Letters 91 (2003) 260602.

45. 45 4.Revolutions after 1995 (3) Direct measurement of thermal noise Fused silica : Structure damping in coating K. Numata et al., Physical Review Letters 91 (2003) 260602.

46. 46 4.Revolutions after 1995 (3) Direct measurement of thermal noise Sapphire : Thermoelastic damping in substrate E.D. Black et al., Physical Review Letters 93 (2004) 241104.

47. 47 4.Revolutions after 1995 (3) Direct measurement of thermal noise Direct measurement of thermal noise of suspension Loss : Resistance of coil-magnet actuator (not material or clamp loss) We can change this resistance. Q-value is still enough high (~10 5 ). K. Agatsuma et al., Physical Review Letters 104 (2010) 040602.

48. 48 (3) Direct measurement of thermal noise 4.Revolutions after 1995 Change of resistance Change of observed sensitivity as theoretical prediction K. Agatsuma et al., Physical Review Letters 104 (2010) 040602. Next step : Thermal noise by loss in suspension itself

49. 49 4.Revolutions after 1995 (4) Reduction of thermal noise Coating thermal noise is the most serious problem ! Coating loss reduction is not so easy … Advanced LIGO : Larger beam LCGT : Cooled sapphire mirror ET : Cooled silicon mirror and larger beam

50. 50 4.Revolutions after 1995 (4) Reduction of thermal noise Amplitude of thermal noise is proportional to (T/Q) 1/2 In general, Q-value depends on T (temperature). We must investigate how dissipation depends on temperature in cryogenic region.

51. 51 4.Revolutions after 1995 (4) Reduction of thermal noise Structure damping in substrate 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.

52. 52 4.Revolutions after 1995 (4) Reduction of thermal noise Structure damping in substrate Fused silica can not be used !

53. 53 4.Revolutions after 1995 (4) Reduction of thermal noise Thermoelastic damping in substrate Thermo-optic noise must be studied …

54. 54 4.Revolutions after 1995 (4) Reduction of thermal noise Structure damping in coating K. Yamamoto et al., Physical Review D 74 (2006) 022002. Loss angle is almost independent of temperature.

55. 55 4.Revolutions after 1995 (4) Reduction of thermal noise Structure damping in coating I. Martin et al., Classical and Quantum Gravity 25(2008)055005. Peak at 20 K ? Annealing suppresses peak (not perfectly). It is assumed that loss is constant.

56. 56 4.Revolutions after 1995 (4) Reduction of thermal noise Structure damping in coating Coating thermal noise is the most serious problem ! Goal temperature : 20 K

57. 57 4.Revolutions after 1995 (4) Reduction of thermal noise How can we cool mirrors ? Sapphire or silicon fiber (high thermal conductivity and high Q-value) CLIO cryostat have already been installed (different scale from that of LCGT and ET).

58. 58 4.Revolutions after 1995 (4) Reduction of thermal noise Within about a week, mirror temperature became about 14 K (mirror temperature must be below 20 K).

59. 59 4.Revolutions after 1995 (4) Reduction of thermal noise Cryocooler Why ? Usual case : Liquid nitrogen and helium Safety and maintenance in mine Cryocooler Usual cryocooler : Gifford-McMahon cryocooler Large vibration Pulse-tube cryocooler (without solid piston) But, vibration of commercial one is not enough small.

60. 60 4.Revolutions after 1995 (4) Reduction of thermal noise Schematic view of silent pulse-tube cryocooler

61. 61 4.Revolutions after 1995 (4) Reduction of thermal noise Measurement of vibration in cryostat with silent pulse-tube cryocooler at silent site Cryocoolers do not increase vibration even if they are put on site with extremely small seismic motion. K. Yamamoto et al., Journal of Physics: Conference Series 32 (2006) 418.

62. 62 5.Summary Long history of research of thermal noise (200 years !) Even now, thermal noise of interferometer is a hot topic. Coating mechanical loss Direct measurement of thermal noise Reduction of thermal noise (cryogenic technique and so on) There are open questions and this field will be hot in future.

63. 63 Thank you for your attention ! Vi ringrazio molto per la vostra attenzione !