1. 1 Kazuhiro Yamamoto Institute for Cosmic Ray Research, the University of Tokyo Cryogenic mirrors: the state of the art in interferometeric gravitational wave detectors 26 May 2011 Gravitational Waves Advanced Detectors Workshop @Hotel Hermitage, La Biodola, Isola d’Elba, Italy

2. 0.Abstract 2 Advantages of cryogenic interferometers (LCGT and ET) (1) Small thermal noise (2) Small thermal lens (3) Less serious parametric instability

3. 3 0.Abstract On July, the special articles (in Japanese !) about LCGT will appear in “Teionkougaku” (Journal of the Cryogenic Society of Japan). Kazuhiro Yamamoto wrote the article which has the same title as that of this talk and will explain outlines of my article in English. (This is the first Japanese article which introduces the technical details of Einstein Telescope, probably.)

4. Contents 1. Introduction 2. Thermal noise 3. Thermal lens 4. Parametric instability 5. Einstein Telescope 6. Summary 4

5. 1.Introduction Generation of interferometric gravitational wave detectors 5 First generation 10 times better sensitivity Second generation 10 times better sensitivity Advanced LIGO, Advanced Virgo, GEO-HF, LCGT Third generation Einstein Telescope (ET) Cryogenic interferometers : LCGT and ET

6. 1.Introduction Why will cryogenic techniques be adopted ? (1) Small thermal noise (2) Small thermal lens (3) Less serious parametric instability 6 At first, these advantages in LCGT are explained. At second, these advantages in ET are summarized.

7. 2.Thermal noise 7 Thermal noise : Fundamental noise around 100 Hz Suspension thermal noise : mirror position fluctuation (vibration of suspension for mirror) Mirror thermal noise : mirror surface fluctuation (elastic vibration of mirror itself)

8. 8 2.Thermal noise 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).

9. 9999 2.Thermal noise Fused silica : mirror substrate material for room temperature interferometers Large mechanical loss at cryogenic temperature Fused silica is not so good in cryogenic interferometers. Sapphire and Silicon : candidates of substrate material for cryogenic interferometers LCGT : Sapphire

10. 10 Suspension thermal noise Sapphire fibers in LCGT Small mechanical dissipation T. Uchiyama et al., Physics Letters A 273 (2000) 310. High thermal conductivity T. Tomaru et al., Physics Letters A 301 (2002) 215. Small suspension thermal noise 2.Thermal noise

11. 11 Mirror thermal noise ”Cryogenics” (K. Numata and K. Yamamoto) in ”Optical Coatings and Thermal Noise in Precision measurements” (Ed. G.M. Harry, T. Bodiya, R. DeSalvo), Cambridge University Press (it will be published soon !) 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 2.Thermal noise

12. 12 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 2.Thermal noise

13. 13 History of research of mirror thermal noise 1997 : First feasibility study for cryogenic interferometer T. Uchiyama et al., Physics Letters A 242 (1998) 211. Drastic progress of research about mirror thermal noise Only substrate Brownian noise was recognized before 1997. It is not trivial that cryogenic technique can reduce mirror thermal noise. 2.Thermal noise

14. 14 Temperature dependence of mirror thermal noise in LCGT Below 20 K : Thermal noise is sufficiently small for LCGT. 2.Thermal noise

15. 15 Sensitivity of LCGT interferometer K. Kuroda et al., Progress of Theoretical Physics Supplement 163 (2006) 54. K. Arai et al., Classical and Quantum Gravity 26 (2009) 204020. Sensitivity is not limited by thermal noise.

16. 16 Thermal lens : Light absorption in mirror Temperature gradient Temperature dependent of refractive index Wave front distortion Worse sensitivity Thermal lens is a serious problem of room temperature interferometers. Advanced LIGO and Virgo : System to compensate thermal lens (compensation plate and ring heater) is necessary. G.M. Harry (for LSC), Classical and Quantum Gravity 27 (2010) 084006. 3.Thermal lens

17. 17 Thermal lens in LCGT Magnitude of thermal lens : P  /  Thermal conductivity (  ) of sapphire at 20 K is 10000 times larger than that of fused silica at 300 K. Temperature coefficient of refractive index (  ) is at least 100 times smaller. Light absorption (P) is almost same (coating dominant). Magnitude of thermal lens is at least 10 6 times smaller. No system for thermal lens compensation is necessary. T. Tomaru et al., Classical and Quantum Gravity 19 (2002) 2045. 3.Thermal lens

18. 18 4. Parametric instability Parametric instability Radiation pressure Modulation (Large amplitude of other (transverse) optical mode) Optical mode in cavity Elastic mode in mirror (Large vibration)

19. 19 4. Parametric instability Parametric instability of LCGT is a less serious problem than that of Advanced LIGO and Advanced Virgo. K. Yamamoto et al., Journal of Physics: Conference Series 122 (2008) 012015. (a) Number of unstable modes is 10 times smaller. (b) Mirror curvature dependence is weaker. Wider safe curvature region (c) More effective passive suppression of instability is possible.

20. 20 4. Parametric instability Number of unstable modes is proportional to the product of elastic and optical mode densities. Elastic mode density of sapphire (LCGT) is 5 times smaller than that of fused silica. Sound velocity in sapphire is larger. (a) Number of unstable modes is 10 times smaller. Optical mode density of LCGT is 2 times smaller. Larger beam is adopted in Advanced LIGO and Advanced Virgo in order to reduce mirror thermal noise.

21. 21 The reason is that smaller beam radius of LCGT. (b) Mirror curvature dependence is weaker. Wider safe curvature region 4. Parametric instability

22. 22 Although number of unstable modes of LCGT is smaller, it is not zero. The tricks to suppress instability is necessary. One of ideas : loss on barrel surface of mirror The increase of thermal noise should be taken into account. Since mirrors of LCGT are cooled, suppression without sacrificing thermal noise is possible. (c) More effective passive suppression of instability is possible. loss on barrel surface 4. Parametric instability

23. 23 Outline of Einstein Telescope Third generation in Europe 10 times better sensitivity than that of LCGT 10 km arm length Xylophone scheme : Two kinds of interferometers Low frequency (LF, 10Hz) and High frequency (HF, 100Hz) LF : Smaller radiation pressure noise, (10 times) smaller light power (than that of LCGT), cryogenic techniques HF : Smaller shot noise, larger light power, without cryogenic techniques 5. Einstein Telescope M. Punturo and H. Lueck, General Relativity and Gravitation 43 (2011) 363. S. Hild et al., Classical and Quantum Gravity 28 (2011) 094013.

24. 24 5. Einstein Telescope Only low frequency interferometer (LF) is discussed. S. Hild et al., Classical and Quantum Gravity 28 (2011) 094013.

25. 25 5. Einstein Telescope Mirror substrate and suspension wire material : Sapphire or Silicon Why is silicon candidate ? Advantage : Larger substrate (radiation pressure noise) Disadvantage : Light wavelength is 1550nm, not 1064nm. Optical properties are not well known. Temperature of mirror is 10 K (LCGT:20 K).

26. 26 5. Einstein Telescope (a) Thermal noise Mirror thermal noise : 10 times smaller Suspension thermal noise : 300 times smaller R. Nawrodt et al., General Relativity and Gravitation 43 (2011) 363. S. Hild et al., Classical and Quantum Gravity 28 (2011) 094013.

27. 27 5. Einstein Telescope (a) Thermal noise Mirror thermal noise : 10 times smaller 3 times longer arm (10 km) 3 times larger beam radius (9cm) Suspension thermal noise : 300 times smaller 3 times longer arm (10 km) 7 times heavier mirror (200 kg) 5 times longer suspension wire (2 m) 100 times smaller dissipation in wires (Q=10 9 )

28. 28 5. Einstein Telescope (b) Thermal lens Magnitude of thermal lens : P  /  Thermal conductivity (  ) at 10 K (ET) is 10 times smaller than that at 20 K (LCGT). Light absorption (P) is 10 times smaller than that of LCGT (coating dominant) because of smaller light power. If ET mirrors are made from sapphire, thermal lens of ET is comparable with that of LCGT. No serious problem

29. 29 Temperature coefficient of refractive index (  ) of silicon is at least 10 times larger than that of sapphire. Thermal lens of ET is at least 10 times larger than that of LCGT. However, even in this case, this is not serious. If ET mirrors are made from silicon … 5. Einstein Telescope B.J. Frey et al., SPIE Conference Proceedings 6273 (2006) 62732J. T. Tomaru et al., Classical and Quantum Gravity 19 (2002) 2045. (b) Thermal lens

30. 30 5. Einstein Telescope Parametric instability : not serious problem Light power is 10 times smaller than that of LCGT. (c) Parametric instability

31. 31 6. Summary LCGT: Sapphire mirrors (20 K) suspended by sapphire fibers (1) Small thermal noise (2) Small thermal lens (3) Less serious parametric instability ET-LF: Silicon or sapphire mirrors (10 K) suspended by silicon or sapphire fibers (1) Small thermal noise : Cryogenic technique, longer baseline, larger beam radius, heavier mass, low loss fibers (2) Small thermal lens (3) Less serious parametric instability : Smaller light power

32. 32 Special thanks to Dr. Kenji Numata (University of Maryland/NASA Goddard Space Flight Center) Dr. Gregory M Harry (Massachusetts Institute of Technology) Dr. Hiroaki Yamamoto (California Institute of Technology) Dr. Takayuki Tomaru (High Energy Accelerator Research Organization) Dr. Harald Lueck (Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut)) Dr. Michele Punturo (Istituto Nazionale di Fisica Nucleare, Sezione di Perugia) Prof. Fulvio Ricci (Universit`a di Roma La Sapienza) Dr. Stefan Hild (University of Glasgow) Dr. Ronny Nawrodt (Friedrich-Schiller-Universitaet Jena)

33. 33 Thank you for your attention !