1. Advanced Gravitational-wave Detector Technologies
Future generations of interferometers
Nergis Mavalvala LIGO Scientific Collaboration GR-17, July 2004

2. GW interferometer at a glance
L ~ 4 km
For h ~ 10–21
DL ~ m
Seismic motion --
ground motion due to natural and anthropogenic sources
Thermal noise --
vibrations due to finite temperature
Shot noise --
quantum fluctuations in the number of photons detected

3. Initial LIGO Sensitivity Goal
Strain sensitivity < 3x /Hz1/2 at 200 Hz
Displacement Noise
Seismic motion
Thermal Noise
Radiation Pressure
Sensing Noise
Photon Shot Noise
Residual Gas
Facilities limits much lower

4. Why a better detector? Astrophysics
Factor 10 to 15 better amplitude sensitivity
(Reach)3 = rate
Factor 4 lower frequency bound
NS Binaries
Initial LIGO: ~ 20 Mpc
Adv LIGO: ~350 Mpc
BH Mergers
Init. LIGO: 10 Mo, 100 Mpc
Adv LIGO: 50 Mo, z=2
Stochastic background
Initial LIGO: WGW ~3e-6
Adv LIGO: WGW ~3e-9

5. Advanced LIGO Target Sensitivity
10 Hz
100 Hz
1 kHz
10-22
10-23
10-24
10-21
Newtonian background
Seismic ‘cutoff’ at 10 Hz
Suspension thermal noise
Test mass thermal noise
Optical noise
Initial LIGO
Advanced LIGO

6. Advanced LIGO The Target The Strategies
Build a detector limited by fundamental noise sources
Gravity gradients at low f
Quantum noise at high f
The Strategies
Seismic noise reduced 40x at 10 Hz
Thermal noise reduced 15x
Optical noise reduced 10x
The Challenges... and overcoming them
Rest of this talk...
LIGO
Advanced LIGO
Seismic
Suspension thermal
Test mass thermal
Quantum
Estimated gravity gradients

7. Detector Overview PRM Power Recycling Mirror BS Beam Splitter
ITM Input Test Mass
ETM End Test Mass
SRM Signal Recycling Mirror
PD Photodiode

8. Seismic Isolation The target The challenge The strategy
Push seismic noise ‘wall’ down to 10Hz
Reduce rms motion at low frequencies (below GW band)
The challenge
Low frequency (few Hz) ground motion ~ few 10-6 m rms
Require displacement of test mass m /Hz at 10 Hz
Need 1010 attenuation of ground noise at 10 Hz
The strategy
Use multi-stage approach to vibration isolation
Active isolation with arrays of sensors and actuators at each stage to measure and suppress vibrations

9. Seismic Isolation Strategy
2 stage active isolation
External pre-isolation
Large dynamic range (1 mm)
Low bandwidth (rms reduction)
In-vacuum active isolation
~1/3 of the required attenuation
~103 reduction of rms in the 1-10 Hz band, crucial for controlling technical noise sources
2 x10-13 m/ Hz at 10 Hz
Mirrors suspended from quadruple pendulum
Provides ~107 attenuation at 10 Hz
6 DOF
hydraulic
quadruple
pendulum
penultimate mass
test mass
BSC vacuum chamber with top removed
ground

10. Optics suspensions and controls
The requirements
Provide additional isolation
Keep suspension thermal noise to a minimum (avoid mechanical dissipation points)
Damp free motions
Provide means for controlling longitudinal and angular positions of mirrors without adding control noise
The strategy
Suspension design to minimize thermal noise
Magnets and coils for position/pointing control
Filter control noise

11. Mirror Suspensions
Multiple pendulum chain ending with the final interferometer mirror
Free motions of mirror suspensions damped using local sensors and actuators
Control noise is filtered by placing sensors and actuators higher up in the chain
Mirror longitudinal and angular positions controlled using “global” signals derived from the interferometric sensing
Global control signals are applied at all stages of the multiple pendulum
Forces are applied from a reaction pendulum to avoid re-introduction of noise

12. Limiting Noise Sources: Thermal noise
Suspended mirror in equilibrium with 293 K heat bath a kBT of energy per mode
Coupling to motion according the fluctuation-dissipation theorem
Any mechanically dissipative system will experience thermally driven fluctuations of its mechanical modes

13. Mechanical dissipation
Gather the energy into a narrow band via low mechanical losses, place resonances outside measurement band
Want f(f), the mechanical loss factor associated with test masses and suspensions, to be small
Thermal displacement spectrum
Detection band
Frequency
pendulum
mode
internal
mode

14. Suspension thermal noise
Monolithic test mass suspensions
40 kg, 32 cm diameter mirrors suspended from four fused silica fibers
Fused silica fibers  ~104x lower loss than steel wire
Ribbon geometry  more compliant along optical axis
Cryogenic suspensions

15. Internal Thermal Noise
Two materials considered for mirror substrates
Sapphire test masses
Much higher Q  2e8 cf. ~2e6 for LIGO I fused silica
BUT higher thermoelastic damping (higher thermal conductivity and expansion coefficients)
Can counter by increasing laser spot size
Developments in size, homogeneity, absorption
Fused silica test masses
Intrinsic Q can be much higher  ~5e7 (must avoid lossy attachments)
Low absorption and inhomogeneity, but expensive
Both materials  mechanical loss from polishing and dielectric coatings being studied and must be controlled

16. Mirrors and Suspensions
30cm
GEO forms a test bed for Advanced LIGO for combination of multiple pendulum suspension design and monolithic suspension technology

17. Limiting Noise Sources: Optical Noise
Shot Noise
Uncertainty in number of photons detected a
Higher circulating power Pbs a low optical losses
Frequency dependence a light (GW signal) storage time in the interferometer
Radiation Pressure Noise
Photons impart momentum to cavity mirrors Fluctuations in number of photons a
Lower power, Pbs
Frequency dependence a response of mass to forces
Shot noise:
Laser light is Poisson distributed  sigma_N = sqrt(N)
dE dt >= hbar  d(N hbar omega) >= hbar  dN dphi >= 1
Radiation Pressure noise:
Pressure fluctuations are anti-correlated between cavities
 Optimal input power depends on frequency

18. Initial LIGO

19. Higher Laser Power The requirement The strategy The challenge
High laser power for good shot noise limited performance
Traded off against radiation pressure noise
The strategy
Increase laser power at input to 180 W  nearly 1 MW of CW power incident on arm cavity optics
The challenge
High power, low noise laser
Power absorption in optics coatings and substrates  absorption and scatter losses for mirror substrates and coatings
Mirror substrate mass  40 kg
LIGO
Advanced LIGO
Seismic
Suspension thermal
Test mass thermal
Quantum

20. Laser Source Require 180 W at output of laser ( 0.8 MW in arms)
End-pumped rod oscillator, injection locked to an NPRO
Prototyping well advanced
½ of slave system has developed 114 W, 87 W single frequency, M2 1.1, polarization 100:1 f 2f QR
YAG / Nd:YAG / YAG
3x 7x40x7 FI
EOM
NPRO
20 W Master BP
High Power Slave
modemaching
optics
YAG / Nd:YAG
3x2x6
output

21. Advanced LIGO Optics The Challenge The Strategy
Higher circulating power 
Absorption in mirror substrates and coatings leads to deformation of mirror geometry according to spatial intensity profile of laser beam
Larger scatter losses for mirror substrates and coatings
Higher displacement noise due to fluctuating laser intensity (radiation pressure)
The Strategy
Develop low absorption and scatter losses for mirror substrates and coatings
Compensation system for thermal distortions due to power absorption
Make the mirrors more massive  40 kg

22. Thermal lensing – the problem
Optical absorption in cylindrical optic leads to thermal gradients because of
Radial variation of laser beam intensity
Radial heat flow to edge of optic
Temperature gradients cause spatial aberrations due to
Non-zero thermal expansion coefficient
Temperature-dependent index of refraction
Deviation from optimal mirror profile limits maximum power that can pass through or be incident on interferometer optic

23. Thermal Compensation
R. Lawrence, MIT
Active thermal compensation schemes to correct for axi-symmetric distortions due to thermal lensing and surface figure errorrs of optics in situ
Auxiliary laser or suspended heating element used to radiatively heat optic
Figures show measured wavefront distortion of a probe laser beam without and with thermal compensation

24. Optical quality of mirrors
Bulk material can have small variations in refractive index due to small variations in crystal axis
Sapphire: birefringent crystal
Correct for index inhomogeneity by
A compensating polish applied to side 2 of sapphire substrate
Reduces the rms variation in bulk homogeneity to ~15 nm rms
Measurement of a 25 cm m-axis sapphire substrate shows the central 150 mm after compensation

25. Signal-recycled Interferometerℓ
Cavity forms compound output coupler with complex reflectivity. Peak response tuned by changing position of SRM
800 kW
125 W
Reflects GW photons back into interferometer to accrue more phase
Signal Recycling
signal

26. Advance LIGO Sensitivity: Improved and Tunable
broadband
detuned narrowband
SQL  Heisenberg microscope analog
If photon measures TM’s position too well, it’s own angular momentum will become uncertain.
thermal noise

27. Summarizing... Seismic noise Thermal noise Optical noise
Active isolation system
Mirrors suspended as fourth (!!) stage of quadruple pendulums
Thermal noise
Suspension  fused quartz; ribbons
Test mass  higher mechanical Q material, e.g. sapphire; more massive (40 kg)
Optical noise
Input laser power  increase to ~200 W
Optimize interferometer response  signal recycling

28. Parameter LIGO I Adv LIGO Equivalent strain noise, minimum
3x10-23/rtHz
2x10-24/rtHz
Neutron star binary inspiral range
20 Mpc
300 Mpc
Stochastic background sens.
3x10-6
1.5-5x10-9
Interferometer configuration
Power-recycled MI w/ FP arm cavities
LIGO I, plus signal recycling
Laser power at interferometer input
6 W
125 W
Test masses
Fused silica, 11 kg
Sapphire, 40 kg
Seismic wall frequency
40 Hz
10 Hz
Beam size
3.6/4.4 cm
6.0 cm
Test mass Q
Few million
200 million
Suspension fiber Q
Few thousand
~30 million

29. Sub-Quantum Interferometers Generation 2++

30. Quantum Noise in Optical Measurements
Measurement process
Interaction of light with test mass
Counting signal photons with a PD
Noise in measurement process
Poissonian statistics of force on test mass due to photons  radiation pressure noise (RPN) (amplitude fluctuations)
Poissonian statistics of counting the photons  shot noise (SN) (phase fluctuations)

31. Free particle SQL
uncorrelated
0.1 MW
1 MW
10 MW

32. Some quantum states of light
Analogous to the phasor diagram
Stick  dc term
Ball  fluctuations
Common states
Coherent state
Vacuum state
Amplitude squeezed state
Phase squeezed state
McKenzie

33. Squeezed input vacuum state in Michelson Interferometer
GW signal in the phase quadrature
Not true for all interferometer configurations
Detuned signal recycled interferometer  GW signal in both quadratures
Orient squeezed state to reduce noise in phase quadrature X+ X- X+ X- X+ X-

34. Back Action Produces Squeezingf
Squeezing produced by back-action force of fluctuating radiation pressure on mirrors
b a
Vacuum state enters anti-symmetric port
Amplitude fluctuations of input state drive mirror position
Mirror motion imposes those amplitude fluctuations onto phase of output field a1 a2
“In” mode at omega_0 +/- Omega  |in> = exp(+/- 2*j* beta) S(r, phi) |out>
Heisenberg Picture: state does not evolve, only operators do. So |out> vacuum state is squeezed by factor sinh(r) = kappa/2 and angle phi = 0.5 arcot(kappa/2).
Spectral densities assuming input vacuum state:
S_b1 = exp(-2 r) ~ 1/kappa when kappa >> 1
S_b2 = exp(+2 r) ~ kappa
S_{b1 b2} = 0

35. Conventional Interferometer with Arm Cavities
Coupling coefficient k converts Da1 to Db2
k and squeeze angle f depends on I0, fcav, losses, f a b
Amplitude  b1 = a1
Phase  b2 = -k a1 + a2 + h
Radiation Pressure
Shot Noise

36. Optimal Squeeze Angle If we squeeze a2
shot noise is reduced at high frequencies BUT
radiation pressure noise at low frequencies is increased
If we could squeeze -k a1+a2 instead
could reduce the noise at all frequencies
“Squeeze angle” describes the quadrature being squeezed
Depends on frequency
RPN dominates at low frequencies
SN dominates at high frequencies
If we could detect frequency-dependent quadrature corresponding to
could remove radiation pressure noise from readout

37. Frequency-dependent Squeeze Angle

38. Squeezing – the ubiquitous fix?
All interferometer configurations can benefit from squeezing
Radiation pressure noise can be removed from readout in certain cases
Shot noise limit only improved by more power (yikes!) or squeezing (eek!)
Reduction in shot noise by squeezing can allow for reduction in circulating power (for the same sensitivity)

39. Squeezed vacuum Requirements Generation methods Challenges
Squeezing at low frequencies (within GW band)
Frequency-dependent squeeze angle
Increased levels of squeezing
Generation methods
Non-linear optical media (c(2) and c(3) non-linearites)  crystal-based squeezing (see ANU poster)
Radiation pressure effects in interferometers  ponderomotive squeezing (in design & planning stages)
Challenges
Frequency-dependence  filter cavities
Amplitude filters
Squeeze angle rotation filters
Low-loss optical systems

40. Sub-quantum-limited interferometerX+ X-
Quantum correlations (Buonanno and Chen)
Input squeezing

41. Other emerging detector technologies
Cryogenic suspensions (LCGT Japan)
Broadband (white light) interferometers (Hannover, UF)
All-reflective interferometers (Stanford)
Reshaped laser beam profiles (Caltech)
Quantum non-demolition
Evade measurement back-action by measuring of an observable that does not effect a later measurement
Speed meters (Caltech, Moscow, ANU)
Optical bars (Moscow)
Correlations between the SN and RPN quadratures