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Discussion of the Advanced LIGO design and sensitivity
Denis Martynov,Massachusetts Institute of Technology
Baikal School on High Energy Physics and Astrophysics July 14, 2016
LIGO Laboratory2
Overview
LIGO optical design Broadband stationary noises
Environmental noises Fundamental noise sources Technical noise sources
Future plans and goals
3
Michelson interferometer
» Measures differential length of two arms using the detector at the antisymmetric port
LIGO Laboratory4
Optical layout
4 km
100 kW
1064 nm
Laser
22W800W
85mW
25mW9MHz
oscillator
5
45MHz
5 longitudinal degrees of freedom• differential arm (GW) • common arm • Michelson interferometer • power recycling cavity • signal recycling cavity
10�14 m
10�12 m
10�6 mGround motion
5
LIGO optical design
» We need nice, robust and low noise instrument
» Quantum noise» Resonators
PD2
Laser
2W
PD1
servo
6
Classical picture of light
100 102 104 106
Frequency, Hz
10-10
10-9
10-8
10-7
10-6
10-5
10-4
Mag
nitu
de, W
/Hz1/
2
Free running laserPD1PD2
P = AA⇤ = (A+ acl)(A⇤ + a⇤cl)
Pac = Aa⇤cl + A⇤acl
where is a static DC fieldis an oscillating AC field (signal or noise)
A
acl
A
PD2
Laser
2W
PD1
servo
7
Classical picture of light
100 102 104 106
Frequency, Hz
10-10
10-9
10-8
10-7
10-6
10-5
10-4
Mag
nitu
de, W
/Hz1/
2
Free running laserPD1PD2Ap
2
Ap2
aclp2
aclp2
aclA
P1 =1
2(Aa⇤cl + A⇤acl)
P2 =1
2(Aa⇤cl + A⇤acl)
PD2
Laser
2W
PD1
servo
8
Classical picture of light
Ap2
Ap2
aclp2
aclp2
aclA
P1 =1
2(Aa⇤cl + A⇤acl)
P2 =1
2(Aa⇤cl + A⇤acl)
100 102 104 106
Frequency, Hz
10-10
10-9
10-8
10-7
10-6
10-5
10-4
Mag
nitu
de, W
/Hz1/
2
Free running laserPD1PD2
PD2
Laser
2W
PD1
servo
9
Classical picture of light
Ap2
Ap2
aclp2
aclp2
aclA
P1 =1
2(Aa⇤cl + A⇤acl)
P2 =1
2(Aa⇤cl + A⇤acl)
100 102 104 106
Frequency, Hz
10-10
10-9
10-8
10-7
10-6
10-5
10-4
Mag
nitu
de, W
/Hz1/
2
Free running laserPD1PD2
PD2
Laser
2W
PD1
servo
10
Classical picture of light
Ap2
Ap2
aclp2
aclp2
aclA
P1 =1
2(Aa⇤cl + A⇤acl)
P2 =1
2(Aa⇤cl + A⇤acl)
100 102 104 106
Frequency, Hz
10-10
10-9
10-8
10-7
10-6
10-5
10-4
Mag
nitu
de, W
/Hz1/
2
Free running laserPD1PD2
PD2
Laser
2W
PD1
servo
11
Quantum picture of light
Ap2
Ap2
A
100 102 104 106
Frequency, Hz
10-10
10-9
10-8
10-7
10-6
10-5
10-4
Mag
nitu
de, W
/Hz1/
2
Free running laserPD1PD2
a1
a2
a1 + a2p2
a1 � a2p2
P1 = Pcl,1 +1
2(A(a⇤1 + a⇤2) + A⇤(a1 + a2))
P2 = Pcl,2 +1
2(A(a⇤1 � a⇤2) + A⇤(a1 � a2))
PD2
Laser
2W
PD1
servo
12
Quantum picture of light
Ap2
Ap2
A a1
a2
a1 + a2p2
a1 � a2p2
P1 = Pcl,1 +1
2(A(a⇤1 + a⇤2) + A⇤(a1 + a2))
P2 = Pcl,2 +1
2(A(a⇤1 � a⇤2) + A⇤(a1 � a2))
100 102 104 106
Frequency, Hz
10-10
10-9
10-8
10-7
10-6
10-5
10-4
Mag
nitu
de, W
/Hz1/
2
Free running laserPD1PD2Shot noise
p2h⌫Pdc
13
Quantum noise in the Michelson interferometer
Laser
DC power at the anti-symmetric portAin
Aas
Pas = Pin sin2 �, where
� = 2⇡x0
�
⌧ 1 is a small detuning
Optical transfer functiondPas
dx
=
Pin
�
4⇡ sin� cos�
Shot noise in units of length is
x
shot
=�
2⇡ cos�
rh⌫
2Pin
= 4.34⇥ 10�18
r125W
P
in
mpHz
ain
aas
14
Fabry-Perot interferometer
Laser
AinAtrAres
Ti Te
Equation of for the intracavity field
Build-up
Ares =p
TiAin +p1� Ti
p1� Te
p1�XAres
b =Ares
Ain=
2pTi
Y, where
Y = Ti + Te +X is the total loss in the cavity
15
Optimal design
» Maximize power in the arms» Minimize power going through the substrates» Filter laser noises» Optimize response in the frequency range
10Hz-10kHz
Laser
Power in the arms is limited by the optical losses1
2GprcGarm =
1
X
Gprc Garm
Garm
LIGO Laboratory16
Quantum noise
101 102 103 104
Frequency, Hz
10-21
10-20
10-19
10-18
10-17
Mag
nitu
de, m
/Hz1/
2 Michelson typeInitial LIGO type
LIGO Laboratory17
Quantum noise
101 102 103 104
Frequency, Hz
10-21
10-20
10-19
10-18
10-17
Mag
nitu
de, m
/Hz1/
2 Michelson typeInitial LIGO type
?
Laser
18
Quantum radiation pressure noise
Power fluctuations in the armAin
aas
Pm =?
Laser
19
Quantum radiation pressure noise
Power fluctuationsAin
vacuum field also resonates and drives suspended mirrorsaas
Pm =p
2h⌫Parmb
Fm =2Pm
c
xm =Fm
M!
2
LIGO Laboratory20
Quantum noise
101 102 103 104
Frequency, Hz
10-21
10-20
10-19
10-18
10-17
Mag
nitu
de, m
/Hz1/
2 Michelson typeInitial LIGO type
?
21
Fabry-Perot interferometer
Laser
ares(t) =p
Tiain(t) + (1� Y
2)ares(t� ⌧)
Equation for the intracavity field
where is the round trip time⌧ =2L
c
⌧ ares +Y
2ares =
pTiain
Solution to this equation is
ares(!) =
pTiain(!)
i!⌧ + Y2
100 102 104
Frequency, Hz
10-2
10-1
100
Mag
nitu
de, W
/W
Y c
8⇡L
LIGO Laboratory22
Advanced LIGO
4 km
100 kW
1064 nm
Laser
22W800W
85mW
25mW9MHz
oscillator
5
45MHz
New mirror
LIGO Laboratory23
Quantum noise
101 102 103 104
Frequency, Hz
10-21
10-20
10-19
10-18
10-17M
agni
tude
, m/H
z1/2 Michelson type
Initial LIGO typeAdvanced LIGO type
24
Noises
» We need to make noises as low as possible» Environmental noises» Fundamental noises» Technical noises
LIGO Laboratory25
Environmental noises
Ground vibrations Gravity gradients Acoustic noise
26
Ground motion
» the motion of the optical table is actively controlled» this motion is passively filtered using multistage
suspensions» gravity gradients are caused by the motion of
chambers, people and the ground
27
Ground motion
10−1 100 10110−14
10−13
10−12
10−11
10−10
10−9
10−8
10−7
10−6
10−5
10−4
Frequency, Hz
Dis
plac
emen
t, m
/Hz1/
2
Ground motion in summerGround motion in winterHAM table in summerHAM table in winterBSC table in summerBSC table in winterGS13 noise
28
Suspension transfer function
10−1 100 10110−7
10−6
10−5
10−4
10−3
10−2
10−1
100
101
Mag
nitu
de (a
bs)
Frequency (Hz)
QUADBSFMHLTSHSTS
LIGO Laboratory29
Scattered light noise
Light scattered out from the main beam gets modulated in phase and amplitude and partially scatters back into the main beam.
20 100 1000 5000Frequency, Hz
10-22
10-21
10-20
10-19
10-18
Dis
plac
emen
t, m
/Hz1/
2
GW signal channelEnd X bulidingEnd Y buildingCorner Station Center and Output AreaCorner Station Input AreaLaser Enclosure
Input test mass
4km
1m
End test mass
LIGO Laboratory30
Fundamental noises
In theory, fundamental noises should limit sensitivity of the instrument
Fundamental sensing noises: Shot noise Residual gas noise
Fundamental displacement noises: Thermal noises Quantum radiation pressure noise
31
Thermal noise
» LIGO operates at room temperature» Thermal motion is proportional to» Arises from finite losses present in
mechanical systems (need high Q)» Thermal motion of the atoms in
suspension fibers moves the mirror
pkT
LIGO Laboratory32
Fundamental noises
101 102 103 104
Frequency [Hz]
10-22
10-21
10-20
10-19
10-18D
ispl
acem
ent [
m/
Hz]
Quantum noiseSeismic noiseGravity GradientsSuspension thermal noiseCoating Brownian noiseCoating Thermo-optic noiseSubstrate Brownian noiseExcess GasTotal noise
LIGO Laboratory33
Technical noises
Technical nosies in the arm cavities include Laser noises Actuator electronics Residual gas in the chambers Angular motion of test masses Charging noise
Auxiliary longitudinal and angular degrees of freedom Input-output port noises
Laser phase and amplitude noises Beam jitter
34
Laser noises
Ideal laser field
Real laser field fluctuates in amplitude and phase
This noise couples to the gravitational wave channel
A(t) = A0sin(!t+ �0)
A(t) = A0(1 +An(t))sin(!t+ �0 + �n(t))
35
Auxiliary degrees of freedom
4 km
100 kW
1064 nm
Laser
22W800W
85mW
25mW9MHz
oscillator
5
45MHz
» Longitudinal from the corner station
» Angular from the arm cavities
LIGO Laboratory36
Low frequency spectrum
LIGO Laboratory37
High frequency spectrum
LIGO Laboratory38
Conclusions
Optical design of the Advanced LIGO is optimized for the frequency range 10Hz - 10kHz
There is an unknown noise source at 20Hz - 100Hz Above 100Hz sensitivity is limited by quantum noise Future goals include the upgrade of the current facility
and construction of a longer facility
https://dspace.mit.edu/handle/1721.1/28646 http://thesis.library.caltech.edu/8899/
39
LIGO Scientific Collaboration
LIGO Laboratory40
Extra slides
LIGO Laboratory41
Charging noise
If mirror surfaces are charged, ambient electric fields couple to gravitational wave channel
Ion gun was developed to discharge the mirrors
Reactionmass
Electrodes
Ringheater
Suspensioncage
HRcoating
Testmass
LIGO Laboratory42
Intensity noise coupling
Laser noises are filtered at 0.6 Hz by the coupled cavity pole. Extra coupling mechanism comes from high-order modes
100 300 600 1000 2000Frequency, Hz
-60
-55
-50
-45
-40
-35
-30
Mag
nitu
de, d
B
LIGO Laboratory43
Noise transients
Electronic failures Seismic noise Acoustic transients Scattered light noise Faulty radio frequency modulators Dust particles
LIGO Laboratory44
Noise transients
LIGO Laboratory45
Beam jitter filtering
Input mode cleaner filters pointing fluctuations
50 100 200 500Frequency, Hz
10-9
10-8
10-7
10-6
10-5
10-4
Ampl
itude
, 1/H
z1/2
46
Future
» What do we ultimately need?
» Medium term goals» Long term goals
47
Squeezed states of light
» reduce quantum noise» inject squeezed vacuum state through the AS port
LIGO Laboratory48
Squeezed states of light Sub-quantum noise level has been demonstrated
3.5 dB squeezing (1.5X reduced noise)
2.1 dB squeezing (1.27X reduced noise)
Typical noise without squeezing Squeezing-enhanced sensitivity
LIGO Laboratory49
Long term goals
Upgrade current facility (LIGO 3) Thermal noise can be reduced by using
cryogenic systems Quantum noise can be reduced by increasing
optical power and mirror masses Feedforward cancellation algorithms can be
applied to gravity-gradient noises
R&D for a longer facility (Lungo)
LIGO Laboratory50
Straw man sensitivity curves
