2

A gravitational wave is a differential strain in spacetime.

Equivalently, it is a differential tidal force that can be sensed by

multiple test masses.

Plus-polarization Cross-polarization

Any system with an accelerating quadrupole moment 𝐼μν:

ℎμν =2𝐺

𝑐4𝑟

d2𝐼μν

d𝑡2 (𝑟 = distance from system to observer)

Inspiral, merger, and

ringdown of binary

systems

Core-collapse

supernovae

Non-axisymmetric

pulsars

4

35 Hz 250 Hz

First aLIGO observing run:

Sep 2015 to Jan 2016

Observed two binary

black hole coalescences

PRL 116, 061102 (2016)

PRL 116, 241103 (2016)

5

Test

masses

Power

recycling

Power recycling increases

the power in the arms

Signal

recycling

Signal recycling broadens

the interferometer’s

sensitivity to GWs

GW readout

125 W laser

source

Basic idea:

Michelson interferometer

Arms are made into

Fabry–Perot cavities

6

101

102

103

Frequency [Hz]

10-24

10-23

10-22

AS

D o

f str

ain

[1

/Hz

1/2

]O1 sensitivity (25 W)Expected sensitivity (125 W)Shot (125 W)Radiation pressure (125 W)Test mass thermalSuspension thermal

7

Test

mass

Test

mass

Test masses,

laser source

8

Test

mass

Beam- splitter

9

10

Layers of SiO2 and Ta2O5

(a few µm total thickness)

High-reflectivity (>99.995%) mirror coatings made with

ion-beam-sputtered thin films

Fused silica substrate

40 kg mirrors made from low-loss fused silica

11

Active

seismic

isolation

Four cascaded pendula give 1/f8 isolation

against seismic noise in the GW band

Top three stages use electromagnetic

actuation

Final stage uses electrostatic actuation

12

Fluctuation–dissipation theorem: thermally-driven

fluctuations are proportional to the system’s losses:

How to reduce thermal noise?

• Use materials with high Q-factors

• Make the laser spot size large

• Exploit “dissipation dilution”

𝑥2 ∝ 𝑇

𝑄

Mean-square

displacement

fluctuation

Temperature

Mechanical Q-factor

Thermal noise arises from: • Test mass coatings

• Test mass substrates

• Suspension fibers

Silica Q ~ 106

Tantala Q ~ 104 Suspension Q ~ 109

13

Seed

crystal

(2 W) Single-pass

amplifier

(35 W)

Injection-

locked

amplifier

(220 W) To vacuum

system

14

35 W single-pass amplifier

220 W injection-locked

amplifier

input modecleaner output

modecleaner

2 W, 1064 nm

seed NPRO main interferometer

fused-silica

reference cavity

24MHz

×59.1MHz

45.5MHz

21MHz

(to test masses)

(from AOM)

(fromAOM)

power

recycling

mirror

signal

recycling

mirror

pre-modecleaner

input test

masses

end test

masses

gravitational

wave readout

Laser power: 125 W of 1064 nm light into interferometer

Laser noise: must contribute no more than one tenth of

the total GW strain ASD

Laser noise affects GW readout because of arm

imbalances:

• Different input test mass reflectivties

• Different arm losses

• Beamsplitter not perfectly 50/50

• Differential arm length offset

15

Freerunning frequency noise is 100 Hz/Hz1/2 at 100 Hz (falls

like 1/f).

Need to suppress this by 8 orders of magnitude at 100 Hz:

Adhikari et al.,

LIGO-T070236

16

Freerunning relative intensity noise is 10–5/Hz1/2 at 100 Hz

(falls like 1/f).

Need to suppress this by 2 orders of magnitude at 100 Hz:

Adhikari et al.,

LIGO-T070236

17

18

Frequency stabilization: Pound–Drever–Hall locking using

three length references:

• Tabletop fused silica reference cavity (20 cm)

• Suspended, in-vacuum ring cavity (16 m)

• Interferometer’s common-mode arm length (4 km)

Common-mode arm length acts like a 4-km-long cavity

with a 1 Hz linewidth

Intensity stabilization: dc locking using three intensity

references:

• Tabletop bow-tie cavity (2.0 m)

• Suspended, in-vacuum ring cavity (16 m)

• [NEW!] Interferometer’s common-mode arm intensity (4

km)

19 101 102 103 104

Frequency [Hz]

10° 9

10° 8

10° 7

10° 6

10° 5

10° 4

asd

of

freq

uen

cy£ H

z/H

z1/2§

Modecleaner shot

Modecleaner length

Interferometer shot

and length noisesFrequency actuator

NPRO, reference cav.Total expected

20

Interferometer optics must be actively controlled in order to maintain

resonance:

• 5 length DOFs

• 20 angular DOFs

In total, there are about 300 servo loops that keep the interferometer

running.

Lowest bandwidth is ~10 mHz (hydraulic compensation of ground

tides)

Highest bandwidth is ~1 MHz (laser noise eater)

21

101 102 103

Frequency [Hz]

10° 21

10° 20

10° 19

10° 18

10° 17

AS

Dof

dis

pla

cem

en

t£ m

/Hz

1/2§

aLIGO H1 freer unning DARM, 2015–12–02 5:30:00 Z

MeasuredQuantum noiseDark noiseSeismic+NewtonianTher malActuator noiseAmbient elect rostat ic

Gas noiseLSCASCIntensi ty+FrequencyJit ter

SRM PEEK (1/ f 1/2)Total expected

22

Different coating materials,

e.g. AlGaAs Squeezed light

Also:

• Heavier test masses (reduces radiation pressure noise)

• Longer suspension fibers (reduces suspension thermal noises)

Nature 7, 962 (2011)

23

Use silicon instead of silica

Operate at 120 K (where thermal expansion

coefficient of silicon is zero)

Use 1.5 µm or 2 µm laser

24

Design with shot noise, radiation pressure noise,

and thermal noise in mind

Laser noise rejection is never perfect in an

interferometer, so crush it with servo loops

The common-mode arm length makes a great

reference cavity

Need better coatings, and possibly a different

laser wavelength

25

2 W seed

crystal

35 W

amplifier

220 W

amplifier

Mode-

cleaning

cavity

Mode-

cleaning

cavity

Laser frequency stabilized

to ~1 µHz/Hz1/2 at 100 Hz

Laser amplitude stabilized

to ~10–8/Hz1/2 at 100 Hz

26

M1

M2

a

For an equal-mass binary,

ℎ ≈4π2𝐺

𝑐4𝑟𝑀𝑎2𝑓0

2

Orbital frequency f0

GW frequency is fGW = 2f0

For M ~ 30M☉, a ~ 100 km, f0 ~ 100 Hz,

and r ~ 500 Mpc, we expect strains of

order 10–21