Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 1 “Colliding Black Holes”, National Center for Supercomputing Applications

1Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006

“Colliding Black Holes”, National Center for Supercomputing Applications

Support: NSF

LIGO – Optical Science and Engineering In Search of Black Holes

David ReitzePhysics DepartmentUniversity of Florida

Gainesville, FL 32611

For the LIGO Science Collaboration


Outline

Overview of gravitational waves» GWs, GW sources and why they’re interesting

Laser interferometry to detect gravitational waves» LIGO Laser Interferometer Gravitational Wave Observatory

» Fundamentals of Interferometry– Noises

» Lasers and Optics in LIGO

Second generation ground-based gravitational wave interferometers» Advanced LIGO

» Challenges in Advanced LIGO


Gravitational Waves

Gravitational Waves: “Odd man out” in general relativity; predicted, but never directly observed.

ds2 = gdxdxghh(r,t) = h+.x exp[i(k.r - t)]

Weak Field Limit: h is a strain: L/L


Gravitational Waves & Electromagnetic Waves: A Comparison

Electromagnetic Waves Time-dependent dipole moment

arising from charge motion

Traveling wave solutions of Maxwell wave equation

Two polarizations: +, -

Spin 1 fields ‘photons’

Gravitational Waves Time-dependent quadrapole

moment arising from mass motion

Traveling wave solutions of Einstein’s equation

Two polarizations: h+, hx

Spin 2 fields ’gravitons’

prrr

trE ˆˆ

4~, 0

),(

2,

4tI

cr

Gth


One Possible Source: Binary Neutron Star Inspiral and Merger

measure masses

and spins of binary system

detect normal modes of

ringdown to identify final NS or BH.

observe strong-field spacetime dynamics, spin

flips and couplings…

Sketch:Kip Thorne

Credit: Jillian Bornak


Other Sources Lurking in the Dark

BANG!

Binary systems» Neutron star – Neutron star» Black hole – Neutron star» Black hole – Black hole

Periodic Sources» Rotating pulsars

“Burst” Sources » Supernovae

– Gamma ray bursts

Residual Gravitational Radiation from the Big Bang

» Cosmic Strings

?????


LIGO Sites

LIGO Livingston Observatory• 1 interferometers

• 4 km arms

• 2 interferometers• 4 km, 2 km arms

LIGO Hanford ObservatoryLIGO Observatories: Caltech and MIT

4 km


Interferometer Network

LIGO

To be six or seven detectors worldwide by 2010-2020.

• Redundancy

• Confidence

• Source location

GEO VirgoTAMA


Fundamentals of LIGO Interferometry

…causing the interference pattern

to change at the photodiode

As a wave passes, the arm lengths change in different ways….

Arms in LIGO are 4 km long Measure difference in

length to one part in 1021 or 10-18 meters


Interferometry: the basics

Simple Michelson

» Phase: = 4 (Lx – Ly) / L

» Power: PPD = PBS sin2– dP/d ~ PBS sin cos

» Strain: h = 2L/L– Phase sensitivity:

d/dh L Lx

Ly

L

PPD X


Beefed-up Interferometry:Fabry-Perot Arm Cavities

Fabry-Perot cavity» Increases power in arms

– Overcoupled cavity gain: GFP ~ 4 / Tinput

» Enhances storage time of light in cavity– Phase shift on resonance– Effectively ‘lengthens’ arms

df/dh GFP x L

Lx

Ly


Advanced Interferometry II:Power Recycling

‘Recycle’ light coming back from beamsplitter» Add a mirror which forms a resonant

cavity with the rest of the interferometer

PBS

= GRC

Pinput

df/dh GFP x L

+

= Enhanced Phase Sensitivity! GRC ~ 50, GFP ~ 80

Lx

Ly

‘Complex Mirror’

5 W

~ 10000 W

250 W


Keeping the Interferometer Together

• All length degrees of freedom must be held on resonance (ie, locked)• heterodyne detection

• reference field provided by electro-optic modulator

• LIGO Interferometers are very complex: 4 length + 10 alignment degrees of freedom• Absolute position must be held to 10-13 m

E = Ein ei 2 cos(mt) E

in [1 + i ei mt + i e-i mt]

m

E

cESB

LaserModulator

LO

Mixer

PDServo electronics

Error Signal

Cavity Length


The LIGO Length Control Scheme

Length Degrees of freedom


Locking the Interferometer•Multiple Input / Multiple Output.

•Four tightly coupled cavities.

•Ill-conditioned (off-diagonal) plant matrix.

•Highly nonlinear response over most of phase space.

•Transition to stable, linear regime takes plant through singularity.

•Employs adaptive control system that evaluates plant evolution and reconfigures feedback paths and gains during lock acquisition. MICH

GO

GO

QPOB

QREFL

SSpob

SSref

glmPob

glmRef

_

_

DARM

CARM

PRC

GOGO

GOGOGO

GOGOGO

QAS

IPOB

IREFL

CasyCasy

CpobCpobSSpob

CrefCrefSSref

gLAsy gLAsy 0

gLPob gLPob glpPob

gLRef gLRef glpRef

_

_

_

1.

2.

POB

REFL AS

GW Signal is measured from DARM Control


Alignment Sensing and Control

Need to also control angular fluctuations x, y of the mirrors x, y for 5 of the 6 interferometer mirrors

Spatially-resolved PDH locking…


Alignment Sensing and Control

Cavity modes U decompose into HG0 and HG1 modes:

» Displacement: U(x) = HG0(x-) HG0(x) + (/wo) HG1(x)

» Tilt: U(x) = HG0(x’) / cos x HG0(x) + i xwo/) HG1(x)

x


The earth is a noisy place

Thermal (Brownian)

Noise

LASER

test mass (mirror)

beamsplitter

Residual gas scattering

Wavelength & amplitude fluctuations

Seismic Noise

Quantum Noise

"Shot" noise

Radiation pressure


‘Noises’ in LIGO

Noise Sources:

• Displacement noise

• Seismic noise

• Radiation Pressure

• Thermal noise

• Suspensions

• Optics

• Sensing Noise

• Shot Noise

• Residual Gas

• Electronic Noise

h(f) = 3 x 10-23 / rHz


Frequency Stabilization in LIGO

Nested control loops» Stage 1 – thermally-20 cm long

stabilized reference cavity» Stage 2 – in vacuum

suspended 12 or 15 m long “mode cleaner’ cavity

» Stage 3 – Fabry Perot arm cavities

f/f ~ 3 x 10-22 @ 100 Hz


LIGO Pre-stabilized Laser


Seismic Noise

Tubular coil springs with internal damping, layered between steel reaction masses

Isolation Performance

Need 10-19 m/rHz @100 Hz


More Seismic isolation

• pendulum design

• provide 102 suppression above 1 Hz

• provide ultraprecise control of optics displacement (< 1 pm)

Mirror Suspensions

Wire standoff & magnet

“OSEM”

LOS

SOS


Thermal NoiseThermal Noise

Dissipative Thermal Noise: the fluctuation-dissipation theorem

tells us that random thermal fluctuations are converted to mechanical motion mirror surfaces, optical coatings, and suspension wires

Extrinsic Thermal Noise: external coupled energy drives thermal motion

» laser power (which fluctuates) couples into mirrors, driving thermal expansion fluctuations in mirrors and optical coatings

therm

diss22

B2diss F

)f(x~f2i)f(Y)}f(YRe{

f

Tk)f(x~


Suspension Thermal Noise

G. Gonzalez, Class. Quantum Grav. 17, 4409-4435 (2000)


Thermal Effects in LIGO Core Optics

Absorption in the mirror substrates and coatings leads to thermal aberrations in the mirrors» Temperature couples to index of

refraction n, thermal expansion T, and photo-elastic stress

E2(r,z)(Reflected from R1)

z

x

wo

R(z)R1

OPL(r)

E1(r,z)(Incident)

E2(r,z)(Transmitted through the substrate)

e

wo

R(z)R1

OPL(r)

E1(r,z)(Incident)

(b)

Mirror

Mirror

(a)

-0.03 -0.02 -0.01 0 0.01 0.02 0.03-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0x 10

-5

Radial Distance (m)

The

rmal

Abe

rrat

ion

(m)

Thermal Aberration

12 th Degree Fit

Optimal Solution


Thermal Effects in LIGO Core Optics

High quality low absorption fused silica substrates

» ~ 2 -10 ppm/cm bulk absorption

» ~ 1-5 ppm coating absorption

– Different for different mirrors

– Can change with time

» All mirrors are different» Unstable recycling cavity

Requires adaptive control of optical wavefronts


Thermal Compensation

CO2



LIGO IS Doing Astrophysics!

~2x10-25

~2x10-25

Upper Limits on the ellipticity of galactic pulsars

Lowest ellipticity limit to date: 4.0x10-7 for PSR J2124-3358 (fgw= 405.6Hz, distance = 0.25 kpc)


Advanced LIGO

At current sensitivity, LIGO detectors are rate-limited

» 0.01 – 1 event per year

Advanced LIGO will increase sensitivity, hence range, by 10X over initial LIGO

» AdvLIGO rate ~ 500X current LIGO

– At least a few EVENTS per year

Anticipate funding to start in 2008, construction to begin in 2011


Enhancements to Advanced LIGO

PRM Power Recycling MirrorBS Beam SplitterITM Input Test MassETM End Test MassSRM Signal Recycling MirrorPD Photodiode

SILICA

40 kg

180 W

830 kW

830 kWQuad Noise Prototype


Advanced LIGO Pre-stabilized Laser

180 W amplitude and frequency stabilized Nd:YAG laser Two stage amplification

» First stage: either MOPA (NPRO + single pass amplifier) or ring cavity (not shown)

» Second stage: injection-locked ring cavity

Developed by Laser Zentrum Hannover (and MPI at Hannover)

front-end output

PZT

BP

high-power laser


Advanced LIGO PSL performance Requirements

» Good spatial mode quality» Intensity stabilization < 3 x 10-9 /rHz» Frequency noise ~ (20 Hz/ f) Hz/rHz

To date» 183 W obtained in good spatial

mode profile (no spatial filtering)» RIN of oscillator @ 3 x 10-9 /rHz

70 80 90 100 110 120 130 140 150 1600,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

M2 < 1.2

wa

ist s

ize

[mm

]

rel. position [mm]


High Power Faraday Isolatorsfor Advanced LIGO

Faraday Isolator designed to handle high average power

» Increased immunity from thermal birefringence

In excess of 40 dB at 100 W loading

» thermal lensing /10 thermal distortions demonstrated /20 possible

0 20 40 60 80 100-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Fo

cal P

ow

er (

m-1)

Incident Power (W)

Rotator only Compensator only Rotator and Compensator

0 20 40 60 80 10015

20

25

30

35

40

45

50

Op

tical Is

ola

tio

n

Incident Laser Power

Current EOT Isolator Compensated Isolator

Isolation versus power

Focal power vs power

Khazanov, et al., J. Opt. Soc. Am B. 17, 99-102 (2000).Mueller, et al., Class. Quantum Grav. 19 1793–1801 (2002).Khazanov, et. al., IEEE J. Quant. Electron. 40, 1500-1510 (2004).

Lens Compensation

FaradayTGG Crystals

TFP TFP/2QR


Interesting physical effects in Advanced LIGO

Stored arm cavity power: 830 kW on resonance» Radiation pressure on resonance:

Frad = 2Pcav/c ~ 6 mN» Leads to (uncontrolled) L = 150 m

3 types of potential instabilities» Optical ‘spring’ effect

– From dynamic force as mirrors go through resonance

» Angular ‘tilt’ Instabilities – From misaligned cavities

» Parametric Instabilities– From excitation of acoustic mirror modes from

higher order cavity modes and

Frad40 kg

L

mg


Optical Spring Effect

For small displacements off resonance, Frad depends linearly on L

Total spring constant felt by mirror is

if ktot < 0, cavity is unstable

Sheard, et al., Phys. Rev. A69 051801 (2004)

Solution for AdvLIGO: higher length servo gain


Angular Instabilities

If cavity beam is displaced, Frad exerts torques on mirrors:

Mirrors act as torsional pendulum

» Solving equations of motions leads to one unstable mode

c

xP2 cav

Solution for AdvLIGO: higher alignment servo gain


Parametric Instabilities

Solution for AdvLIGO: acoustic damping, thermal ROC tuning

Coupling of intracavity photon-acoustic modes

» High intracavity powers excite acoustic modes in the mirrors (Stokes mode)

» Instability depends on– Intracavity power – Substrate material

Speed of sound, mechanical Q – Cavity parameters

Length, mirror RoC

Parametric Gain; R> 1 leads to instability

V. B. Braginsky, et al., Phys. Lett. A, 305, 111, (2002);C. Zhao, et al, Phys. Rev. Lett. 94, 121102 (2005).

TM acoustic mode TEM 10 mode


The LIGO Science Collaboration


Conclusions

Acknowledgments

• Members of the LIGO Laboratory, members of the LIGO Science Collaboration, National Science Foundation

More Information

• http://www.ligo.caltech.edu; www.ligo.org

• LIGO is operational and taking data as we speak

• ½ way through S5 Science Run

• Gravitational wave detection pushes state-of-the art in CW

solid state laser technology, optical fabrication and metrology,

and control systems

• Advanced LIGO design is well underway

Documents

Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 1 “Colliding Black Holes”, National Center for Supercomputing Applications