LIGO-G1401365-v1
Koji Arai – LIGO Laboratory / Caltech

Ph.D at Univ of Tokyo (1995-1999)
 Design & build of TAMA300 double-pendulum suspensions
 Interferometer length sensing for power recycled Fabry-Perot
Michelson Interferometer

Commissioning and science runs of TAMA300
interferometer (1999-2009)

@LIGO Caltech (2009-)
Output mode cleaner development
eLIGO/aLIGO commissioning

Mission:
To convey technical knowledge necessary for building
and operating the LIGO India detector, or similar
interferometer, including prototypes

by going through:
 the common technologies in laser interferometer
GW detectors
 Detailed description / discussion about the
interferometer sensing & control
Lecture plan
DAY1 General overview of laser interferometer GW detectors
Interferometer configurations
DAY2 Noises in GW detectors
DAY3 Control system & its modeling
DAY4 Interferometer length sensing and control
Feedforward noise cancellation
Quantum noise
DAY5 Higher-order laser modes

General Relativity
 Gravity = Spacetime curvature
 Gravitational Wave = Wave of spacetime curvature

GW
 Generated by motion of massive objects
 Propagates with speed of light
 Cause quadrupole deformation
of the spacetime
Free
mass
GW

What does the balls feel?
 The balls are free mass (= free falling)
 ...Geodesic lines
GW

Q. What happens
if the balls are connected
by bars
Free
mass


Michelson-type interferometers are used
Differential change of the arm path lengths
=>change interference
condition
Mirror
Beamsplitter
Laser
Mirror
Interference
Fringe

p
p iWL/ c
b2( W
a ( W) + p E0
1 )−= Re2iWL/
c
e p Rec2iWL/
− cR 2 ✓
2
Te2iWL/
2w
!
p
1
−
T
1
−
p E0 TeiWL/ cpRe 2w x ( W)
b2(eW
) = c − pR
a2( W2) + ◆
2iWL/
2iWL/ c
p 1 − Re
p 1 − Re2iWL/0c
b2( W) =
a2( W) + p E0 T
c
c
1 − Re2iWL/ c
T
1 − Re2iWL/
!
p
✓
◆
g + iW
2
2/ pT
! 2w0 x ( W)
p E0 ◆
b2( W) =
a2( W) + ✓
iW ✓
2
2wc0 x ( W
! T
g g− +iW
g
p 1 − 2/iW/
pT E2/
b2(g(at
W+) iW
=
a2( W2) + ◆
low
frequencies)
0
T1 − iW/
2w0gx ( W) c
g
−
iW
T
p
b2( W) =
a2( W) +
E0
g − iW
1 − iW/ g
c
T
e1 = ex cos qcos f + ey cos qsin f − ez cos q
eyfcos qsin f − ez cos q
e2e1= =−exexcos
sinqcos
f + fey+cos
e1 = ex cos qcos f + ey cos qsin f − ez cos q
e2 = − ex sin f + ey cos f
e2 = − ex sin f + ey cos f
e2
⇥
⇤
F+ = e⇥
e
−
e
e
: [e1e1 − e2e2]
x x
y y ⇤
⇥
⇤
F
=
e
e
−
e
e
+
x
x
y
1 −e2ee21e]2]
F
=
e
e
−
e
e
: [:e[1ee12e+
⇥
x x
y y y⇤
e1
⇥
F⇥ = ex ex − ey ey : [e1e2 + e2e1]
Antenna pattern
Low-Frequency AntennaPattern
z
θ
!
y
q
Frms =
2
F+2 + F⇥
x
Rev. Mod. Phys. 86 (2014) 121-151
http://link.aps.org/doi/10.1103/RevModPhys.86.121
(http://arxiv.org/abs/1305.5188)



The effect of GW is very small
h ~ 10-23 => distance of 1m changes 10-23m
Corresponds to:
change by ~0.01 angstrom (or 1pm)
for distance between the sun and the earth
1.5 x 1011 m
changes
by 1/100 of a H atom diameter!
Mirror


GW Detection = Length measurement
The longer arms, the bigger the effect
 GW works as strain => dx = hGW x Larm
 Until cancellation of the signal happens
in the arms
 Optimum arm length
Mirror
Mirror
Larm = 75km (for fGW =1kHz)
Laser
Laser
4Larm = lGW (= c / fGW )
Photodetector
Photodetector
Mirror

LIGO Observatories
Hanford / Livingston 4km
Still shorter than the optimum length
=> Use optical cavity to increase life time of the photons in the arm
\
c.f. Virgo (FRA/ITA) 3km, KAGRA (JPN) 3km, GEO (GER/GBR) 600m

“Still simplified” LIGO Interferometer
4km
Fabry-Perot
Cavity
Vacuum Chamber /
Beam tube
4km Fabry-Perot Cavity
Mirror Suspension
Beamsplitter
Recycling
Mirrors
Laser
Mode
Cleaner
L~16m
Photodetector
Digital Control System
Vibration
Isolation
System
Data Acquisition
/Analysis System
Mirror




3 fundamentals of the GW detector
Mechanics
Optics
Electronics




3 fundamentals of the GW detector
Mechanics
Optics
Electronics

An IFO produces a continuous signal stream
in the GW channel

The detector is fixed on the ground
=> can not be directed to a specific angle

GWs and noises are, in principle, indistinguishable
=> Anything we detect is GW

Reduce noises!


Obs. distance is inv-proportional to noise level
x10 better => x10 farther => x1000 more galaxies

Sensitivity (=noise level) of Enhanced LIGO
Laser shot noise
Laser radiation
pressure
noise
thermal noise
seismic noise
Laser intensity
/frequency noise
h= 2x10-23 /rtHz
electronics noise
digitization noise
angular control noise
......

aLIGO sensitivity
Preliminary
x= 4x10-20 m/rtHz
h= 1x10-23 /rtHz

Compact Binary Coalescence
=> Chirp signal
 NS-NS binaries
Accurate waveforms predictable
(Post Newtonian approximation)
=> Template banks & Matched
Filter analysis (amplitude & phase
information)
 BH-BH binaries
Similar waveforms,
but more difficult to predict
because of earlier merging
Mat]ched filtering analysis
B. F. Schutz, “Gravitational wave astronomy”,
10-15
Spectral sensitivity (strain per root Hz)
10
2-1 6
0M
Class. Quantum Grav. 16 (1999) A131.
o BH
at z
=1
-16
f_ISCO = 1/(pi (6 M)^3/2)
10-17
10-18
LISA
10 6
M
10-19
o -10
M
o BH
10-20
at z
=
2 -1
1
Crab (1 yr)
0M
GEO600
o BH
at 2
10-21
binary confusion background
10-22
10-23
00
Mp
2-0
c
.5M
o BH
at 2
2-N
0M
Sa
pc
t 20
0M
pc
r) c
1 y Mp
(
0
1
X- at 2
o
Sc ode NS f-mode at 20Mpc
r-m
(10-4Moc2 energy)
Sc
LIGO II
10
-24
Stochastic background,
2-detector sensitivity --
10-25
10-6
10-5
10-4
10-3
10-2
10-1
Wgw =10-14
100
gravitational wave frequency (Hz)
101
LIGO I
oX
Wgw =10-10
102
103
-1
(1 d
ay )
Wgw =10-6
104

Binary inspiral range
 Chirp waveform PSD
: Dist ribut ion of inspiral horizon dist ance for t he four gravit at ional wave det ect ors H1, L1, H2 and V1 for all of S5
SR1. T his hist ogram includes each 2048-second analyzed segment from S5 and VSR1. T he dist ribut ions shown here
ond t o t he 1.4 -1.4 solar mass inspiral horizon dist ance for t he LIGO det ect ors. For t he V irgo det ect or, we have plot t ed
-1.0 solar mass inspiral horizon dist ance dist ribut ion, scaled by (2.8/ 2) 5/ 6 t o adjust for t he lower mass.
 ISCO freq (HF cut off freq)
M is t he chirp mass of t he binary, D is t he dist ance t o t he binary and is a real funct ion of f , paramet rized
e t ot al mass M . Set t ing h⇢i = 8 and insert ing t his waveform int o eqn. 3, we find t hat t he inspiral horizon
ce is given by
s Z
✓
◆1/ 2
f h i gh
1 5⇡
f − 7/ 3
5/ 6 − 7/ 6
D=
(GM ) ⇡
4
df ,
(6)
8 24c3
Sn (f )
f l ow
 Horizon range (Integrated SNR of 8)
D is expressed in Mpc. T he inspiral horizon dist ance is defined for opt imally locat ed and orient ed sources.
uniform dist ribut ion of source sky locat ions and orient at ions, we divide t he inspiral horizon dist ance by 2.26 t o
t he SenseMon range [9] report ed as a figure of merit in t he LIGO and Virgo cont rol rooms.
iLIGO 15Mpc
ract ice, it is convenient t o measure dist ances in Mpc and mass in M . It is useful t herefore t o specialize eqn.
his unit syst em. Furt her, since we measure t he st rain h(t) at discret e t ime int ervals eLIGO
∆ t = 1/ f s ,20Mpc
t he spect ral
y is only known wit h a frequency resolut ion of ∆ f = f s / N , where N is t he number of dat a point s used t o
aLIGO
50Mpc
re Sn (f https://dcc.ligo.org/LIGO-T0900499/public
). By put t ing f = k∆ t int o eqn. 6 and grouping t erms by unit s, we arrive at t he
expression
 In the control room we use D/(2.26)
taking all sky average

LIGO-Virgo only
From LIGO-G1201135-v4

LIGO-Virgo plus LIGO-India
From LIGO-G1201135-v4

Burst gravitational waves
 Supernovae, binary merger phase, etc
Accurate waveforms unpredictable
=> Find signals with an “unusual” amplitude
=> Important to distinguish from non-stationary noises

Continuous waves
 Pulsars
Sinusoidal signal with some modulations
=> Longterm integration
=> Important to distinguish from line noises
(Remark: power line freq. US 60Hz, India 50Hz)

Stochastic gravitational wave background
 From early universe
The waveforms are random
=> Correlation analysis of the detector network
=> The total GW flux can be estimated
=> Or, skymap of the flux is obtained from radiometric
analysis

In all cases, it is highly desirable to have
the detectors to have comparable sensitivities

GWs ~ ripples of the spacetime

Not yet directly detected
~ the effect is so small (h<10-21)

Michelson-type interferometers are used

GW detection is a precise length
(=displacement) measurement!

GW effect is very small

Basically, the larger, the better.
LIGO has two largest interferometers
in the world, and the third one will have
very important role in GW astronomy

IFO consists of many components
Optics / Mechanics / Electronics
and their combinations (e.g. Opto-Electronics)

Noises and signals are, in principle, indistinguishable.
Noise reduction is essential