1. Laser interferometric gravitational wave detectors
The search for the elusive wave
Nergis Mavalvala
(LIGO Scientific Collaboration)
NYUAD, Jan 2010

2. Outline
Gravitational waves (GWs)
Sources
Detectors
(Sampling of) astrophysical searches
Next generation detectors
Confronting quantum measurement limits
Detectors in space

3. Gravitational wave (GW) basics
Gravitational Waves are a prediction of general relativity “Ripples in spacetime fabric” traveling at speed of light
Stretch and squeeze the space transverse to direction of propagation
Strain
Emitted by aspherical accelerating masses
Like tides  for objects that are free to move, GWs change lengths by fractional amounts
Like tides  GWs change lengths by fractional amounts

4. Astrophysics with GWs vs. Light
Very different information, mostly mutually exclusive
Difficult to predict GW sources based on EM observations
Light GW
Accelerating charge
Accelerating mass
Images
Waveforms
Absorbed, scattered, dispersed by matter
Very small interaction; matter is transparent
100 MHz and up
10 kHz and down

5. Astrophysical sources of GWs
Ingredients
Lots of mass (neutron stars, black holes)
Rapid acceleration (orbits, explosions, collisions)
Colliding compact stars
Merging binaries
Supernovae
The big bang
Earliest moments
The unexpected
GWs
neutrinos
photons
now

6. Gravitational waves -- the Evidence
Hulse & Taylor’s Binary Neutron Star System
(discovered in 1974, Nobel prize in 1993)
PSR
Two neutron stars orbiting each other at c
Compact, dense, fast  relativistic system
Emit GWs and lose energy
Used time of arrival of radio pulses to measure change in orbital period due to GW emission
Change in orbital period
NS rotates on its axis 17 times/sec. Reaches periastron (minimum separation of binary pair) every 7.75 hours.
Systematic variation in arrival time of pulses. Variation in arrival time had a 7.75 hour period  binary orbit with another star.
Pulsar clock slowed when traveling fastest and in strongest part of grav field (periastron).
Figure shows decrease in orbital period of 76 usec/year. Shift in periastron due to decay of orbit.
Y-axis = change in orbital period relative to 1975 measurement
Define periastron as measure of orbital period
Exactly as predicted by GR for GW emission
Years

7. In our galaxy (21 thousand light years away, 8 kpc)
Strength of GWs
Hulse-Taylor binary pulsar at the end of its lifetime (100 million years from now)
In our galaxy (21 thousand light years away, 8 kpc)
h ~ 10-18
In the Virgo cluster of galaxies (50 million light years away, 15 Mpc)
h ~ 10-21 M r R

8. Interferometric detectors
Laser
Photodetector
GW from space
Laser
Photodetector
1000 times smaller than the nucleus of an atom

9. Measurement and the real world
How to measure the gravitational-wave?
Measure the displacements of the mirrors of the interferometer by measuring the phase shifts of the light
What makes it hard?
GW amplitude is small
External forces also push the mirrors around
Laser light has fluctuations in its phase and amplitude

10. GW detector at a glance Seismic noise
Ground motion (natural and anthropogenic)
Vibration isolation
20 kW
Thermal noise
Vibrations due to finite temperature
Low mechanical dissipation
Shot noise
Operate on dark fringe
High circulating power
10 W

11. 10 kg Fused Silica 25 cm diameter 10 cm thick < lambda/5000
over beam diameter

12. Some (small) numbers
Sensitivity: m/√Hz at 150 Hz rad/√Hz at 150 Hz
Actuation range: ~100 µm (tides)
Stabilization of 4 km arms: m rms
Laser intensity noise (RIN): ≤10-8 /√Hz at 150 Hz
Frequency noise: ≤ 3×10-7 Hz/√Hz at 150 Hz
Angular Control: ≤ 10-8 rad rms
Angular Sensing: radians/√Hz at 40 Hz
Input beam jitter: ≤4×10-9 rad/√Hz at 150 Hz
Mechanical loss angle: suspension ≤ optical coatings ≤ substrate ≤10-6

13. Initial LIGO (2005 to 2007) Initial LIGO Seismic noise Thermal noise
Ground vibrations
Initial LIGO
Thermal noise
Damped pendulum
Shot noise
Photon counting
SQL:
h(f) = sqrt(8*hbar/M)/Omega/L
Sounds – 200 Hz, 440 Hz, 1 kHz, 10 kHz
Standard
Quantum
Limit

14. Global network of detectors
GEO
VIRGO
LIGO
TAMA
AIGO
LIGO
Detection confidence
Source polarization
Sky location
LISA

15. Gravitational-wave searches
Instrument and data

16. Science runs and sensitivity
1st Science Run
Sept 02
(17 days) S2
2nd Science Run
Feb – Apr 03
(59 days) S3
3rd Science Run
Nov 03 – Jan 04
(70 days)
Strain (sqrt[Hz]-1)
LIGO Target Sensitivity S5
5th Science Run
Nov 05 onward
(1 year integrated) S4
4th Science Run
Feb – Mar 05
(30 days)
Frequency (Hz)

17. Science runs and Sensitivity

18. Astrophysical searches
Coalescence of binary compact objects (neutron stars, black holes, primordial BH)
Core collapse supernovae
Black hole normal mode oscillations
Neutron star rotational instabilities
Gamma ray bursts
Cosmic string cusps
Periodic emission from pulsars (esp. accretion driven)
Stochastic background (incoherent sum of many sources or very early universe)
Expect the unexpected!
Transient
Campanelli et al., Lazarus Project
GWs
neutrinos
photons
now
High duty cycle

19. Sampling of current GW searches
Stochastic Background

20. Cosmological GW Background
385,600
10-22 sec
10+12 sec
Waves now in the LIGO band were produced sec after the Big Bang
WMAP 2003

21. Stochastic GW background
What’s our Universe made of?
Elements in the early Universe
10-5
10-6
Dark matter 23%
Initial LIGO (2 year data)
Atoms 4%
Speculative structures (cosmic strings)
10-8
Energy density in GWs
GWs ??
10-9
Advanced LIGO (1 year data) S4
Sensitivity scales as sqrt(BW*T_int) for Omega, or fourth-root(BW*T_int) for strain.
S5 Nature result = 6.9e-6 (Nature 460, , 2009)
Dark energy 73%
10-13
Inflation
f ~ 100 Hz

22. Example of current GW searches
Binary Inspirals

23. Gamma-ray Bursts GRB 070201 Looked for a GW signal in LIGO
Short, hard gamma-ray burst
Consistent with being in M31
Leading model for short GRBs: binary merger involving a neutron star
Looked for a GW signal in LIGO
Searched for both inspiral and burst signals
No plausible GW signal found
Abbott et al., Ap. J 681, 1419 (2008)
Conclusion: it was most likely an SGR giant flare in M31
Mazets et al., Ap. J 680, 545 (2008)
Ofek et al., Ap. J 681, 1464 (2008)
This is the improved position localization, using Konus-Wind, INTEGRAL and MESSENGER
Leading model for short hard GRBs: binary merger involving a neutron star (found in giant elliptical galaxies, too old (> 5 Gyr to be supernovae). SHBs in non-star-forming region or gaint ellipticals which contain large population of LMXBs that accrete and merge. Core collapse in young, star forming regions.
Significance of extragalactic SGR giant flares as origin of some short hard GRBs
The LIGO result is mentioned in these papers as evidence against a merger
Ofek et al.: “Given the properties of this GRB, along with the fact that LIGO data argue against a compact
binary merger origin in M31, it is an excellent candidate to have been an extragalactic SGR giant flare…. However, we cannot rule out the possibility that it was a short-duration GRB in the background.”
Mazets et al.: Title of paper (paraphrased) is: “A giant flare from an SGR in M31”
IPN 3-sigma error region from Mazets et al., ApJ 680, 545

24. Search for Binary Inspirals
Number of galaxies
Distance (~50 Mly)
Initial LIGO
Sources
Binary neutron stars (~1 – 3 Msun)
Binary black holes (< 30 Msun)
Primordial black holes (< 1 Msun)
Search method
Look for “chirps”
Limit on rate at which NS are coalescing in galaxies like our own
BBH
BNS
Here shown is inspiral range – averaged over all sky
BNS inspiral horizon distance – two 1.4 Msun NS optimally oriented, SNR =8
For binary black hole searches the effective distance is for two 5 Msun BHs optimally oriented with SNR =8.
50 Mly is about 15 Mpc. So units of the Kalogera graph is distance to Virgo cluster.
The S5 results are quoted in terms of blue solar luminosity, L_10. The MW has ~1.7*L_10.
The rate of compact binary coalescences is expected to be proportional to be the blue light luminosity of a galaxy. L_10 is 10^10 times the blue solar luminosity.
The S5 result is < per year per L10 or 0.039*1.7 = per year per MWEG.
S5  R < per year per MW-like galaxy
24 galaxies like our Milky Way S4

25. Next generation detectors
Advanced LIGO

26. Ultimate limits ? Seismic gravity gradient
When ambient seismic waves pass near and under an interferometric gravitational-wave detector, they induce density perturbations in the Earth, which in turn produce fluctuating gravitational forces on the interferometer’s test masses.
Human gravity gradient
The beginning and end of weight transfer from one foot to the other during walking produces the strongest human-made gravity-gradient noise in interferometric gravitational-wave detectors (e.g. LIGO). The beginning and end of weight transfer entail sharp changes (time scale τ∼20 msec) in the horizontal jerk (first time derivative of acceleration) of a person’s center of mass.

27. Beyond Initial LIGO
Shot noise
Quantum radiation pressure noise

28. Advanced LIGO improvements
Seismic noise
Active isolation system
Mirrors suspended as fourth (!!) stage of quadruple pendulums
Thermal noise
Suspension  fused quartz; ribbons
Test mass  higher mechanical Q material; more massive (40 kg)
Optical noise
Laser power  increase to ~200 W
Optimized interferometer response  signal recycling

29. Origin of the Quantum Noise Vacuum fluctuations
Quantum nature of light

30. Advanced LIGO Quantum noise everywhere
Radiation pressure noise
Stronger measurement  larger backaction
Shot noise
More laser power  stronger measurement

31. Quantum states of light
Coherent state (laser light)
Squeezed state
Two complementary observables
Make on noise better for one quantity, BUT it gets worse for the other
X1 and X2 associated with amplitude and phase uncertainty X1 X2

32. Quantum Noise in an Interferometer
Caves, Phys. Rev. D (1981)
Slusher et al., Phys. Rev. Lett. (1985)
Xiao et al., Phys. Rev. Lett. (1987)
McKenzie et al., Phys. Rev. Lett. (2002)
Vahlbruch et al., Phys. Rev. Lett. (2005)
Radiation pressure noise
Quantum fluctuations exert fluctuating force  mirror displacement X1 X2
Laser X1 X2
Shot noise limited  (number of photons)1/2
Arbitrarily below shot noise X1 X2 X1 X2
Vacuum fluctuations
Squeezed vacuum

33. Squeezing injection in Advanced LIGO
Laser
GW Detector
SHG
Faraday isolator
Squeezing
source
The squeeze source drawn is an OPO squeezer, but it could be any other squeeze source, e.g. ponderomotive squeezer.
OPO
Homodyne Detector
Squeeze
Source
GW Signal

34. Advanced LIGO with squeeze injection
Radiation pressure
Shot noise

35. How to squeeze?
My favorite way
A tight hug

36. How to squeeze photon states?
Need to simultaneously amplify one quadrature and de-ampilify the other
Create correlations between the quadratures
Simple idea  nonlinear optical material where refractive index depends on intensity of light illumination

37. Squeezed Input Interferometer
Laser
GW Detector
SHG
Faraday isolator
The squeeze source drawn is an OPO squeezer, but it could be any other squeeze source, e.g. an optical parametric oscillator.
OPO
Homodyne Detector
Squeeze
Source
GW Signal

38. Squeezed state generation
Vacuum (shot)
Noise power (dBm/rtHz)
Squeezed
Dark
Time (s)
Frequency (Hz)
Goda et al., Opt. Lett. (2008)
Vahlbruch et al., New J. Phys. 9, 371 (2007)

39. Squeezing injection in a prototype interferometer
K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K.McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, Nature Physics 4, 472 (2008)
2.9 dB or 1.4x

40. Radiation pressure the other quantum noise
Quantization of mirror states?

41. Optical cooling and trapping of mirrors
Low mass movable mirror
Detuned optical cavity with high circulating laser power
Radiation pressure
Restoring force (trap)
Damping force (cool)
Quantum states of mirrors
Path to observing quantum states for mirrors

42. Optically trapped and cooled mirror
Optical fibers
Teff = 6.9 mK N = 105
Mechanical Q = 20000
Cooling factor larger than mechanical Q because Gamma = Omega_eff/Q. The OS increases Omega but doesn’t affect Gamma (OS is non-mechanical), so Q must increase to keep Gamma constant.
1 gram mirror
T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett 99, (2007)

43. Cooling the kilogram-scale mirrors of Initial LIGO
Teff = 1.4 mK N = 234
Mr ~ 2.7 kg ~ 1026 atoms
Wosc = 2 p x 0.7 Hz
LIGO Scientific Collaboration

44. Space observatories
LISA DECIGO

45. LISA (mid to late 2010’s)

46. Opportunities
Most sensitive GW telescopes with user community of few 100 scientists
Advanced LIGO has hardware (and software/pipeline) contributions from international partners
R&D for third generation detectors needs to be done now
Gravity gradients
Underground observatories?
Active cancellation?
Optics and quantum nondemolition techniques
High laser power systems
(Non)linear optics
Thermal noise mitigation
Super-materials?
Cryogenic operation
The LIGO Scientific Collaboration:

47. When the elusive wave is captured…
Tests of general relativity
Waves  direct evidence for time-dependent metric
Black hole signatures  test of strong field gravity
Polarization of the waves  spin of graviton
Propagation velocity  mass of graviton
Astrophysics
Predicted sources: compact binaries, SN, spinning NS
Inner dynamics of processes hidden from EM astronomy
Dynamics of neutron stars  large scale nuclear matter
The earliest moments of the Big Bang  Planck epoch
Precision measurement below the quantum noise limit

48. The End

49. Photon counting statistics Radiation pressure noise
Beyond initial LIGO
Shot noise
Photon counting statistics
Radiation pressure noise
Fluctuating photon number exerts a fluctuating force