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Detectors Kazuhiro Yamamoto Insitute for Cosmic Ray Research, The University of Tokyo KAGRA Summer School Lectures 30 July 2014 @University of Toyama, Toyama, Japan 1 References (English book) P.R. Saulson, “Fundamentals of Interferometric Gravitational Wave Detectors” World Scientific Pub Co Inc (1994) M. Maggiore, “Gravitational Waves: Volume 1 : Theory and Experiments”, Oxford University Press (2007) Edited by D.G. Blair, E.J. Howell, L. Ju, C. Zhao, “Advanced Gravitational Wave Detectors” Cambridge University Press (2012) 2 Reference (Japanese book) 中村 卓史、三尾 典克、大橋 正健 編 “重力波をとらえる ---存在の証明から検出へ” 京都大学出版会 (1998). 3 Reference (Review paper) R. X. Adhikari, “Gravitational radiation detection with laser interferometry” Review of Modern Physics 86 (2014) 121-151. 4 0.Abstract I would like to explain … (1) Resonator as oldest type of detector (2) Interferometer as commonest type detector (3) Fundamental noise of interferometer 5 Contents 1. Introduction 2. Resonator 3. Interferometer 4. Fundamental noise of interferometer 5. Summary 6 1.Introduction 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) 7 1.Introduction Gravitational wave Speed is the same as that of light. Transverse wave and two polarizations http://spacefiles.blogspot.com 8 1.Introduction 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 9 1.Introduction 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 10 2.Resonator Resonant detector Gravitational wave excites resonant motion of elastic body. Weber bar (commonest one) “300 years of gravitation” (1987) Cambridge University Press Fig. 9.8 Diameter : several tens cm Length : a few meters Resonant frequency : about 1 kHz 11 2.Resonator Joseph Weber (1919-2000) Pioneer of gravitational wave detection He is one of persons who proposed the concept of laser. Other persons (C.H. Townes, N.G. Basov, A.M. Prokhorov) won Nobel prize in Physics (1964). He started development of resonant detector. J. Weber, Physical Review 117 (1960) 306. 12 2.Resonator Weber event J. Weber, Physical Review Letters 22 (1969) 1302. “Evidence for discovery of gravitational radiation” Coincidence between two detectors (Distance is 1000 km) Direction of sources : Center of our galaxy 13 2.Resonator However, … Theorists pointed out that our galaxy disappears in short period if center of galaxy emits so large energy. No experimentalists could confirm Weber event even if they used detectors with better sensitivity ! We do not know what caused Weber event, but gravitational wave did not. 14 2.Resonator List of resonators First generation (room temperature) University of Maryland (U.S.A.) … Second generation (4 K) Explorer (Italy, CERN), Allegro (U.S.A.), Niobe (Australia), Crab (Japan) … Third generation (< 100 mK) Nautilus (Italy), Auriga (Italy), Mini-Grail (Netherlands), Mario Schenberg (Brazil) … This is not a perfect list ! 15 2.Resonator List of resonators First generation (room temperature) University of Maryland (U.S.A.) … Second generation (4 K) Explorer (Italy, CERN), Allegro (U.S.A.), Niobe (Australia), Crab (Japan) … Third generation (< 100 mK) Nautilus (Italy), Auriga (Italy), Mini-Grail (Netherlands), Mario Schenberg (Brazil) … 16 Exploler G. Pizzella, ET first general meeting (2008) 17 NAUTILUS INFN - LNF G. Pizzella, ET first general meeting (2008) 18 2.Resonator AURIGA Padova G. Pizzella, ET first general meeting (2008) 19 2.Resonator Mini-Grail About 3 kHz http://www.minigrail.nl/ Mario Schenberg O.D. Aguiar et al., Classical and Quantum Gravity 25 (2008) 114042. 20 2.Resonator Old but original resonators in Japan (Not bar and sphere) One of examples : Torsion detector (60 Hz) “Gravitational wave detection” Kyoto University Press (1998) Fig. 5-6. (Japanese) S. Kimura et al., Physics Letters A 81 (1981) 302. Best upper limit of continuous gravitational wave from Crab pulsar h<2*10-22 (Until 2008) T. Suzuki, “Gravitational Wave Experiments” World Scientific p115 (1995). 21 3.Interferometer Interferometer (on Earth) Gravitational wave changes length difference of two arms. Frequency : 10 Hz – 10 kHz 22 3.Interferometer Brief early history of interferometer “300 years of gravitation”(1987) Cambridge University Press Idea or suggestion F.A.E. Pirani (1956), Gertsenshtein and Pustovoit (1962), J. Weber (mid-1960’s) First interferometric detector G.E. Moss, L.R. Miller, R.L. Forward, Applied Optics 10 (1971) 2495. Detailed design and feasibility study R. Weiss (1972) https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=38618 23 3.Interferometer Longer baseline is better. However, budget is larger ! At most, baseline is on the order of km … km km How can we enhance effective baseline length ? 24 3.Interferometer Effective baseline length enhancement D.R. Herriott, H.J. Schulte, Applied Optics 4 (1965) 883. D.Shoemaker et al., Physical Review D 38 (1988) 423. R.W.P. Drever, in Lecture Notes in Physics (Springer-Verlag, Berlin), Vol 124, p 321-338 (1983). R.W.P. Drever, in The Detection of Gravitational Waves (Cambridge University Press), p 306 (1991). 25 3.Interferometer Effective baseline length enhancement All current interferometers have Fabry-Perot cavities. Issues of Delay-line : Larger mirror, Scattered light Issues of Fabry-Perot (control of mirror) was solved by Drever himself (Pound-Drever-Hall method for Fabry Perot cavity control, Applied Physics B 31(1983)97) and followers. 26 3.Interferometer Trivia Pound-Drever-Hall method, Applied Physics B 31(1983)97. Web site of Nobel foundation 27 3.Interferometer Rainer Weiss Wikipedia (English) Ronald W.P. Drever They shared Einstein Prize (2007, American Physical Society) “For fundamental contributions to the development of gravitational wave detectors based on optical interferometry, leading to the successful operation of the Laser Interferometer Gravitational Wave Observatory.” http://www.aps.org/programs/honors/prizes/einstein.cfm 28 3.Interferometer Power recycling (reduction of shot noise) Power recycling mirror R.W.P. Drever et al., in Quantum Optics, Experimental Gravity, and Measurement Theory, (Plenum, New York, 1983), p. 503. 29 3.Interferometer Signal Recycling and Resonant Sideband Extraction (change of interferometer response to gravitational wave) Signal recycling mirror B. J. Meers, Physical Review D 38 (1988) 2317. J. Mizuno et al., Physics Letters A 175 (1993) 273. 30 3.Interferometer List of interferometers First generation (past) LIGO (U.S.A.), VIRGO (Italy and France), GEO (Germany and U.K.), TAMA (Japan), CLIO (Japan) Second generation (present or near future, first detection) Advanced LIGO (U.S.A.), Advanced VIRGO (Italy and France), GEO-HF(Germany and U.K.), KAGRA (Japan) Third generation Einstein Telescope (Europe), LIGO III(U.S.A.) 31 3.Interferometer Sensitivity of km scale interferometer 1st generation This graph is old one. 10 times 2nd generation 10 times 3rd generation 32 First and second generation interferometers LIGO (4 km) Advanced LIGO GEO (600 m) GEO-HF TAMA (300 m) KAGRA (3 km) CLIO (100 m) LIGO (4 km) Virgo (3 km) Advanced LIGO Advanced Virgo 33 3.Interferometer First generation : LIGO (U.S.A.) 4 km, Hanford and Livingston (3000 km distance) (U.S.A.) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 34 3.Interferometer First generation : VIRGO (Italy and France) 3 km, Pisa (Italy) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 35 3.Interferometer First generation : GEO (Germany and U.K.) 600 m, Hannover (Germany) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 36 3.Interferometer First generation : TAMA (Japan) 300 m, Tokyo (Japan) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 37 3.Interferometer First generation : CLIO (Japan) 100 m, Kamioka (Japan) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 38 3.Interferometer Second generation Observation (km scale) : Soon ! We can expect first detection ! Advanced LIGO, Advanced VIRGO Upgrade of LIGO and VIRGO GEO-HF(Germany and U.K.), Upgrade of GEO (Now GEO-HF is only one interferometer in operation) KAGRA (Japan) Cryogenic technique Underground site (small seismic motion) 39 Location of KAGRA 3 km, Kamioka (Japan) KAGRA is planed to be built underground at Kamioka, where the prototype CLIO By K. Kuroda (2009 May Fujihara seminar) detector is placed. 40 3.Interferometer CLIO (Japan) Prototype for KAGRA (cryogenic technique, same underground site) S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 41 3.Interferometer Third generation Einstein Telescope (Europe) 30 km vacuum tube in total Cryogenic technique Underground site (small seismic motion) LIGO Scientific Collaboration study : LIGO III (U.S.A.) 42 3.Interferometer Schedule M. Punturo et al., Classical and Quantum Gravity 27 (2010) 084007. 43 4.Fundamental noise of interferometer Interferometric gravitational wave detector Mirrors must be free and are suspended. S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001. 44 4.Fundamental noise of interferometer Typical example of sensitivity of 2nd generation interferometer (KAGRA old one) http://spacefiles.blogspot.com 45 4.Fundamental noise of interferometer Seismic noise Vibration of ground shakes mirrors. 46 4.Fundamental noise of interferometer Thermal noise Mirrors and suspension are in heat bath. Random energy flow from heat bath Limit from statistical mechanics 47 4.Fundamental noise of interferometer Quantum noise Quantum amplitude and phase fluctuations of light Limit from quantum mechanics 48 4.Fundamental noise of interferometer Seismic noise Vibration of ground shakes mirrors. How can we reduce seismic noise ? (1) Small seismic motion site (2) Good vibration isolation system 49 4.Fundamental noise of interferometer Seismic noise (1) Small seismic motion site Where is silent sites ? Underground ! Kamioka mine M. Punturo, GWDAW Rome 2010 BFO (Black Forest Observatory): -162m BRG (Berggieshübel seism Observatory): -36m GRFO (Graefenberg borehole station): -116m Kamioka (Kamioka mine): -1000m 50 4.Fundamental noise of interferometer Seismic noise (1) Small seismic motion site Outside of mine <1 Hz (Outside of mine) =(Center of mine) >1 Hz (Outside of mine) >(Center of mine) Vertical motion is similar to horizontal one. . 51 4.Fundamental noise of interferometer Seismic noise (1) Small seismic motion site Inside of mine > 50 m Silent sufficiently ! Main mirrors 50 m from ground (KAGRA : 200m) 52 4.Fundamental noise of interferometer Seismic noise (2) Good vibration isolation system Mirrors are suspended. Slow motion Mirror follows motion of support point. Fast motion Mirror can not follow motion of support point. 53 4.Fundamental noise of interferometer Seismic noise (2) Good vibration isolation system Transfer function : (Motion of mirror)/(Motion of support) 54 4.Fundamental noise of interferometer Seismic noise (2) Good vibration isolation system VIRGO: Super Attenuator Unfortunately, single pendulum does not have enough isolation for gravitational wave detection. We need multi stage isolation system. Mirror M. Punturo, GWDAW Rome 2010 55 4.Fundamental noise of interferometer Seismic noise (2) Good vibration isolation system R. X. Adhikari, Review of Modern Physics 86 (2014) 121-151. Vibration isolation in detectors 4.Fundamental noise of interferometer Thermal noise Mirrors and suspension are in heat bath. Random energy flow from heat bath Limit from statistical mechanics 57 4.Fundamental noise of interferometer Thermal noise Most famous example of thermal motion : Brown motion Robert Brown investigated random motion of small particles (~1 mm) in water. R. Brown, Philosophical Magazine 4 (1828) 161. Albert Einstein showed theory of Brownian motion. A. Einstein, Annalen der Physik 17 (1905) 549. Relation between diffusion of particles (fluctuation) and viscosity of water (dissipation). 58 4.Fundamental noise of interferometer Thermal noise 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 59 4.Fundamental noise of interferometer Thermal noise Basis of thermal noise of interferometric detector Thermal noise of suspension and mirror 60 4.Fundamental noise of interferometer Thermal noise Suspension and mirror : Mechanical harmonic oscillator Resonant frequency : suspension : ~ 1 Hz mirror : > 10 kHz Target frequency of gravitational wave : ~ 100 Hz Off resonance thermal noise Residual gas damping is not a problem because interferometer in vacuum (< 10-7 mbar). Mechanical loss in suspension and mirror is crucial. 61 4.Fundamental noise of interferometer Thermal noise 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. 62 4.Fundamental noise of interferometer Thermal noise 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. 63 4.Fundamental noise of interferometer Thermal noise Measurement of Q-value (Decay time of resonance motion) We can derive thermal noise spectrum from measured Q-values and Fluctuation-Dissipation Theorem. 64 4.Fundamental noise of interferometer Thermal noise Reduction of thermal noise In the case of mirror thermal noise … Advanced LIGO and Virgo : Larger beam KAGRA : Cooled sapphire mirror ET (low frequency): Cooled silicon mirror and larger beam ET (high frequency): Room temperature fused silica mirror and larger beam Larger beam Large beam observes wide area. Correlation between the motions at center and at edge of beam is small.65 4.Fundamental noise of interferometer Thermal noise Reduction of thermal noise Cooled mirror Amplitude of thermal noise is proportional to 1/2 (T/Q) In general, Q-value depends on T (temperature). We must investigate how dissipation depends on temperature in cryogenic region. 66 4.Fundamental noise of interferometer Thermal noise Reduction of thermal noise Goal temperature (KAGRA) : 20 K 67 4.Fundamental noise of interferometer Thermal noise Demonstration of thermal noise reduction by cooling mirror in CLIO ! T. Uchiyama et al., Physical Review Letters 108 (2012) 141101. 4.Fundamental noise of interferometer Quantum noise Quantum amplitude and phase fluctuations of light Limit from quantum mechanics 69 4.Fundamental noise of interferometer Quantum noise What generates quantum fluctuation of light ? Interference between light and vacuum fluctuation Phase and amplitude fluctuation Phase fluctuation : Shot noise Gravitational wave shifts phase of light. 4.Fundamental noise of interferometer Quantum noise Amplitude fluctuation : Radiation pressure noise http://spacefiles.blogspot.com Photons come at random (amplitude fluctuation). Back action of photon is also at random. → Radiation pressure noise 71 4.Fundamental noise of interferometer Quantum noise How do shot and radiation pressure noise depend on laser power (P)? shot noise ~ P ~m 1 quantum noise with 100x increased laserpower ~ P Standard Quantum Limit (SQL) Lower limit of summation of shot noise and radiation pressure noise 72 4.Fundamental noise of interferometer Quantum noise There is an optimal power of light. However, this value is higher than usual laser power. Development of high power laser (~100 W) is in progress. Power recycling is also useful. 73 4.Fundamental noise of interferometer Quantum noise There is an optimal sensitivity. (Shot noise) ~ (Radiation pressure noise) So far, in typical cases, (Shot noise) >> (Radiation pressure noise) It is not easy to observe radiation pressure noise. Observation itself is an interesting topic. We can observe larger radiation pressure noise with lighter mirrors. 74 4.Fundamental noise of interferometer Quantum noise Latest result Radiation pressure noise of 5 mg mirror is observed ! (KAGRA : 23 kg) N. Matsumoto et al., arXiv 1312.5031 N. Matsumoto, GWADW2014 http://www.gravity.ircs.titech.ac.jp/GWADW2014/slide/Nobuyuki_Matsumoto.pdf 75 4.Fundamental noise of interferometer Quantum noise Radiation pressure noise of 5 mg mirror is observed ! http://www.gravity.ircs.titech.ac.jp/GWADW2014/slide/Nobuyuki_Matsumoto.pdf N. Matsumoto will give talk the progress after this experiment on Friday afternoon. 76 4.Fundamental noise of interferometer Quantum noise After observation of radiation pressure noise …. Beyond Standard Quantum Limit There are many method to beat Standard Quantum Limit. H.J. Kimble et al., Physical Review D 65 (2001) 022002. 5.Summary Nobody has detected gravitational wave directly. Resonant (around kHz or 60Hz) and interferometric detectors (10Hz- 10kHz) were constructed on Earth and are operated for observation. We expect that 2nd generation interferometers will detect finally ! Three kinds of fundamental noise of interferometer; Seismic noise, Thermal noise, Quantum noise (1) Seismic noise : Silent site and excellent vibration isolation system 78 5.Summary Three kinds of fundamental noise of interferometer; Seismic noise, Thermal noise, Quantum noise (2) Thermal noise : Evaluation : Q measurement and Fluctuation-Dissipation Theorem Reduction : High Q, Larger beam, Cooled mirror (3) Quantum noise : Shot noise : High power laser and power recycling Radiation pressure noise : Observation with mg mirror Standard Quantum Limit : We can beat it ! 79 Thank you for your attention ! 80