Kazuhiro Yamamoto

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Cryogenic mirrors the state of the art in
interferometeric gravitational wave detectors
Kazuhiro Yamamoto Institute for Cosmic Ray
Research, the University of Tokyo
26 May 2011 Gravitational Waves Advanced
Detectors Workshop _at_Hotel Hermitage, La
Biodola, Isola dElba, Italy
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0.Abstract
Advantages of cryogenic interferometers
(LCGT and ET)
(1) Small thermal noise (2) Small
thermal lens (3) Less serious
parametric instability

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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.)
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Contents

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

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1.Introduction

• Generation of interferometric gravitational wave
  detectors

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
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1.Introduction

• Why will cryogenic techniques be adopted ?
• (1) Small thermal noise
• (2) Small thermal lens
• (3) Less serious parametric instability

At first, these advantages in LCGT are explained.
At second, these advantages in ET are
summarized.
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2.Thermal noise
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)

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

Sensitivity of LCGT interferometer
Sensitivity is not limited by thermal noise.
K. Arai et al., Classical and Quantum Gravity 26
(2009) 204020.
K. Kuroda et al., Progress of Theoretical Physics
Supplement 163 (2006) 54.
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3.Thermal lens
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.
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3.Thermal lens
Thermal lens in LCGT
T. Tomaru et al., Classical and Quantum Gravity
19 (2002) 2045.
Magnitude of thermal lens P b / k
Thermal conductivity (k) of sapphire at 20 K
is 10000 times larger than that of fused
silica at 300 K.
Temperature coefficient of refractive index (b)

is at least 100 times smaller.
Light absorption (P) is almost same (coating
dominant).
Magnitude of thermal lens is at least 106
times smaller.
No system for thermal lens compensation is
necessary.
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4. Parametric instability
Parametric instability
Radiation pressure
Optical mode in cavity
Elastic mode in mirror
(Large amplitude of other (transverse) optical
mode)
(Large vibration)
Modulation
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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.
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4. Parametric instability
(a) Number of unstable modes is 10 times smaller.
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.
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.
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4. Parametric instability
(b) Mirror curvature dependence is weaker.
Wider safe
curvature region
The reason is that smaller beam radius of LCGT.
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4. Parametric instability
(c) More effective passive suppression
of
instability is possible.
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
loss on barrel surface
The increase of thermal noise should be taken
into account.
Since mirrors of LCGT are cooled, suppression
without sacrificing thermal noise is possible.
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5. Einstein Telescope
Outline of 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.
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
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5. Einstein Telescope
S. Hild et al., Classical and Quantum Gravity 28
(2011) 094013.
Only low frequency interferometer (LF) is
discussed.
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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 (LCGT20 K).
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5. Einstein Telescope
(a) Thermal noise Mirror thermal noise 10 times
smaller Suspension thermal noise 300 times
smaller
S. Hild et al., Classical and Quantum Gravity 28
(2011) 094013.
R. Nawrodt et al., General Relativity and
Gravitation 43 (2011) 363.
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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
(Q109)
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5. Einstein Telescope
(b) Thermal lens
Magnitude of thermal lens P b / k
Light absorption (P) is 10 times smaller than
that of LCGT (coating dominant) because of
smaller light power.
Thermal conductivity (k) at 10 K (ET)
is 10 times smaller than that
at 20 K (LCGT).
If ET mirrors are made from sapphire, thermal
lens of ET is comparable with that of LCGT. No
serious problem
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5. Einstein Telescope
(b) Thermal lens
If ET mirrors are made from silicon
Temperature coefficient of refractive index (b)
of silicon is at least 10 times
larger than that of sapphire.
B.J. Frey et al., SPIE Conference Proceedings
6273 (2006) 62732J.
Thermal lens of ET is at least 10 times larger
than that of LCGT. However, even in this case,
this is not serious.
T. Tomaru et al., Classical and Quantum Gravity
19 (2002) 2045.
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5. Einstein Telescope
(c) Parametric instability
Parametric instability not serious problem
Light power is 10 times smaller than that of
LCGT.
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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
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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
(Universita di Roma La Sapienza) Dr. Stefan Hild
(University of Glasgow) Dr. Ronny Nawrodt
(Friedrich-Schiller-Universitaet Jena)
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Thank you for your attention !