Download KAGRA summer school (Yamamoto 2014)

Detectors
Kazuhiro Yamamoto
Insitute for Cosmic Ray Research, The University of Tokyo
KAGRA Summer School Lectures
30 July 2014 @University of Toyama, Toyama, Japan
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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)
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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).
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Reference (Review paper)
R. X. Adhikari,
“Gravitational radiation detection with laser interferometry”
Review of Modern Physics 86 (2014) 121-151.
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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
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Contents
1. Introduction
2. Resonator
3. Interferometer
4. Fundamental noise of interferometer
5. Summary
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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)
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1.Introduction
Gravitational wave
Speed is the same as that of light.
Transverse wave and two polarizations
http://spacefiles.blogspot.com
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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
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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
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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
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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.
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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
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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.
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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 !
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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) …
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Exploler
G. Pizzella, ET first general meeting (2008)
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NAUTILUS
INFN - LNF
G. Pizzella, ET first general meeting (2008)
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2.Resonator
AURIGA
Padova
G. Pizzella, ET first general meeting (2008)
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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.
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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).
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3.Interferometer
Interferometer (on Earth)
Gravitational wave changes length difference of two arms.
Frequency : 10 Hz – 10 kHz
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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
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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 ?
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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).
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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
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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
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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.
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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.)
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3.Interferometer
Sensitivity of km scale interferometer
1st
generation
This graph is old one.
10 times
2nd generation
10 times
3rd generation
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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
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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.
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3.Interferometer
First generation : VIRGO (Italy and France)
3 km, Pisa (Italy)
S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.
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3.Interferometer
First generation : GEO (Germany and U.K.)
600 m, Hannover (Germany)
S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.
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3.Interferometer
First generation : TAMA (Japan)
300 m, Tokyo (Japan)
S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.
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3.Interferometer
First generation : CLIO (Japan)
100 m, Kamioka (Japan)
S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.
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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)
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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.
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3.Interferometer
CLIO (Japan)
Prototype for KAGRA
(cryogenic technique, same underground site)
S. Kawamura, Classical and Quantum Gravity 27 (2010) 084001.
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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.)
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3.Interferometer
Schedule
M. Punturo et al., Classical and Quantum Gravity 27 (2010) 084007.
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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.
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4.Fundamental noise of interferometer
Typical example of sensitivity
of 2nd generation interferometer (KAGRA old one)
http://spacefiles.blogspot.com
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4.Fundamental noise of interferometer
Seismic noise
Vibration of ground
shakes mirrors.
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4.Fundamental noise of interferometer
Thermal noise
Mirrors and
suspension are
in heat bath.
Random energy
flow from heat bath
Limit from
statistical mechanics
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4.Fundamental noise of interferometer
Quantum noise
Quantum amplitude
and phase
fluctuations of light
Limit from
quantum mechanics
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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
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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
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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.
.
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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)
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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.
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4.Fundamental noise of interferometer
Seismic noise
(2) Good vibration isolation system
Transfer function : (Motion of mirror)/(Motion of support)
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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
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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
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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).
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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
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4.Fundamental noise of interferometer
Thermal noise
Basis of thermal noise of interferometric detector
Thermal noise of suspension and mirror
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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.
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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.
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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.
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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.
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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.
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4.Fundamental noise of interferometer
Thermal noise
Reduction of thermal noise
Goal temperature (KAGRA) : 20 K
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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
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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
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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
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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.
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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.
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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
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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.
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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
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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 !
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Thank you for your attention !
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