Detection of Gravitational Waves with Interferometers

1. Detection of Gravitational Waves with Interferometers Three generations of instruments Nergis MavalvalaMITMarch 2004

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

3. Gravitational Waves • General relativity predicts transverse space-time distortions propagating at speed of light • In TT gauge and weak field approximation, Einstein field equations  wave equation • Conservation laws • Conservation of energy  no monopole radiation • Conservation of momentum  no dipole radiation • Lowest moment of field  quadrupole (spin 2) • Radiated by aspherical (“dark) astrophysical objects • Push freely floating masses together and apart

4. Astrophysics with GWs vs. E&M • Very different information, mostly mutually exclusive • Difficult to predict GW sources based on EM observations

5. Emission of gravitational radiation from PSR1913+16 due to loss of orbital energy period sped up 14 sec from 1975-94 measured to ~50 msec accuracy deviation grows quadratically with time Nobel prize in 1997  Taylor and Hulse Gravitational waves measured?

6. R M M r h ~10-21 Strength of GWs:e.g. Neutron Star Binary • Gravitational wave amplitude (strain) • For a binary neutron star pair

7. Effect of a GW on matter

8. 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

9. GW detector at a glance L ~ 4 km For h ~ 10–21 DL ~ 10-18 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

10. Initial LIGO Sensitivity Goal • Strain sensitivity < 3x10-23 1/Hz1/2at 200 Hz • Displacement Noise • Seismic motion • Thermal Noise • Radiation Pressure • Sensing Noise • Photon Shot Noise • Residual Gas • Facilities limits much lower

11. 3 0 3 ( ± 0 1 k 0 m m s ) LIGO WA 4 km 2 km LA 4 km

13. Limiting Noise Sources:Seismic Noise • Motion of the earth few mm rms at low frequencies • Passive (and active) seismic isolation • amplify at mechanical resonances • but get isolation above 10 Hz (0.10 Hz)

14. damped springcross section Seismic Isolation • Cascaded stages of masses on springs (same principle as car suspension)

15. FRICTION Limiting Noise Sources: Thermal Noise • Suspended mirror in equilibrium with 293 K heat bath akBT of energy per mode • Fluctuation-dissipation theorem: • Dissipative system will experience thermally driven fluctuations of its mechanical modes: • Low mechanical loss (high Quality factor) • Suspension  no bends or ‘kinks’ in pendulum wire • Test mass  no material defects in fused silica Z(f) is mechanical impedance (loss)

16. Optics Suspension andControl • Suspension is the key to controlling thermal noise • Magnets and coils to control position and angle of mirrors

17. Core Optics Installation and Alignment • Cleanliness of paramount importance

18. Limiting Noise Sources: Optical Noise • Shot Noise • Uncertainty in number of photons detected a • Higher circulating power Pbsa low optical losses • Frequency dependence a light (GW signal) storage time in the interferometer • Radiation Pressure Noise • Photons impart momentum to cavity mirrorsFluctuations in the number of photons a • Lower input power, Pbs • Frequency dependence a response of mass to forces  Optimal input power depends on frequency

19. Initial LIGO

20. Light bounces back and forth along arms ~100 times 20 kW DL = h L h ~ 10-21 Light is “recycled” ~50 times 300 W input test mass GW Interferometer end test mass Laser + optical field conditioning signal 6Wsingle mode 4 km All cavities on resonance  interferometer is “locked”

21. Stabilized Laser Custom-built 10 W Nd:YAG laser — Now a commercialproduct Stabilization cavities and servo loops

22. LIGO Optics Substrates: SiO2 • High purity, low absorption • f = 25 cm, mass = 10.8 kg Polishing • Accuracy < 1 nm • Micro-roughness < 0.1 nm Coating • Scatter < 50 ppm • Absorption < 0.5 ppm • Uniformity <10-3 (~1 atom/layer) Industrial partnerships • 2 manufacturers of fused silica • 4 polishers • 5 metrology companies/labs • 1 optical coating company

23. S2 2nd Science Run Feb - Apr 03 (59 days) S1 1st Science Run Sept 02 (17 days) Strain (1/rtHz) LIGO Target Sensitivity S3 3rd Science Run Nov 03 – Jan 04 (70 days) Frequency (Hz) Science Runs and Sensitivity DL = strain x 4000 m 10-18 m rms

24. LIGO Science Has Started • LIGO has started taking data • Science runs (S1, S2, S3) • Inspirals  reach > few Mpc • Stochastic background  limits on Wgw < 10-2 • Periodic sources  limits on hmax ~ few x 10-23(e ~ few x 10-6 @ 3.6 kpc) • Reach design sensitivity • Advanced LIGO

25. Advanced LIGO

26. The next-generation detectorAdvanced LIGO (aka LIGO II) • Now being designed by the LIGO Scientific Collaboration • Goal: • Quantum-noise-limited interferometer • Factor of 15 increase in sensitivity • Factor of 3000 in event rate One day > entire2-year initial data run • Schedule: • Begin installation: 2007 • Begin data run: 2009

27. Quantum LIGO I LIGO II Test mass thermal Suspension thermal Seismic A Quantum Limited Interferometer

28. How will we get there? • 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, e.g. sapphire; more massive (40 kg) • Optical noise • Input laser power  increase to ~200 W • Optimize interferometer response signal recycling

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

31. Advance LIGO Sensitivity:Improved and Tunable broadband detunednarrowband thermal noise

32. Thorne… Advance LIGO: Source specific

33. Sub-Quantum InterferometersAdvanced LIGO ++

34. 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+ X+ X+ Squeezed input vacuum state in Michelson Interferometer

35. Ponderomotive squeezing 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 X- X+ Input vacuum state gets squeezed in an interferometer X- X+

36. X- X+ Sub-quantum-limited interferometer Quantum correlations Input squeezing

37. LISA Laser Interferometer Space Antenna

38. Laser Interferometer Space Antenna (LISA) • Three spacecraft • triangular formation • separated by 5 million km • Formation trails Earth by 20° • Approx. constant arm-lengths • Constant solar illumination 1 AU = 1.5x108 km

39. LISA and LIGO

40. Gravitational-waves Instruments Tests of General Relativity Quantum Measurement Astrophysics

41. Ultimate success…New Instruments, New Field, the Unexpected…

42. With losses

43. Production of squeezed light • Non-linear crystals • Optical Parametric Amplification (OPA) • Three wave mixing • Pump (532nm) • Seed (1064nm)

44. OPA Process • Phase dependent • Lines of force • Compresses along phase axis • Stretches along amplitude axis

45. Squeezing Experimental Schematic

46. Proposed squeezing experiment

47. GWs neutrinos photons now Analysis working groups  Sources • Inspiral • Coalescing compact binaries • Periodic • Periodic continuous waves • Burst • Triggered • Untriggered • Stochastic • Primordial Big Bang background • Continuum of sources