1. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 1 “Colliding Black Holes”, National Center for Supercomputing Applications Support: NSF LIGO – Optical Science and Engineering In Search of Black Holes David Reitze Physics Department University of Florida Gainesville, FL 32611 For the LIGO Science Collaboration

2. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 2 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

3. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 3 Gravitational Waves Gravitational Waves: “Odd man out” in general relativity; predicted, but never directly observed. ds 2 = g   dx   dx  g     h  h(r,t) = h +.x exp[i(k. r -  t)] Weak Field Limit: h is a strain:  L/L

4. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 4 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 +, h x Spin 2 fields  ’gravitons’

5. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 5 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

6. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 6 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 ?????

7. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 7 LIGO Sites LIGO Livingston Observatory 1 interferometers 4 km arms 2 interferometers 4 km, 2 km arms LIGO Hanford Observatory LIGO Observatories: Caltech and MIT 4 km

8. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 8 Interferometer Network LIGO To be six or seven detectors worldwide by 2010-2020. Redundancy Confidence Source location GEO Virgo TAMA

9. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 9 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 10 21 or 10 -18 meters

10. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 10 Interferometry: the basics Simple Michelson »Phase:  = 4  (L x – L y ) /    L »Power: P PD = P BS sin 2  –dP/d  ~ P BS sin  cos  »Strain: h = 2  L/L –Phase sensitivity: d  /dh  L LxLx LyLy LL P PD X

11. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 11 Beefed-up Interferometry: Fabry-Perot Arm Cavities Fabry-Perot cavity »Increases power in arms –Overcoupled cavity gain: G FP ~ 4 / T input »Enhances storage time of light in cavity –Phase shift on resonance –Effectively ‘lengthens’ arms df/dh  G FP x L LxLx LyLy

12. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 12 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 P BS = G RC P input df/dh  G FP x L + = Enhanced Phase Sensitivity! G RC ~ 50, G FP ~ 80 LxLx LyLy ‘Complex Mirror’ 5 W ~ 10000 W 250 W

13. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 13 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 = E in e i 2  cos(  m t)  E in [1 + i  e i  m t + i  e -i  m t ] mm EcEc ESBESB Laser Modulator LO Mixer PD Servo electronics Error Signal Cavity Length

14. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 14 The LIGO Length Control Scheme Length Degrees of freedom

15. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 15 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. 1. 2. POB REFL AS GW Signal is measured from DARM Control

16. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 16 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…

17. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 17 Alignment Sensing and Control Cavity modes U decompose into HG 0 and HG 1 modes: »Displacement: U(x) = HG 0 (x-  )  HG 0 (x) + (  /w o ) HG 1 (x) »Tilt: U(x) = HG 0 (x’ ) / cos  x  HG 0 (x) + i  x  w o / ) HG 1 (x)  xx

18. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 18 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

19. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 19 ‘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

20. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 20 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

21. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 21 LIGO Pre-stabilized Laser

22. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 22 Seismic Noise Tubular coil springs with internal damping, layered between steel reaction masses Isolation Performance Need 10 -19 m/rHz @100 Hz

23. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 23 More Seismic isolation pendulum design provide 10 2 suppression above 1 Hz provide ultraprecise control of optics displacement (< 1 pm) Mirror Suspensions Wire standoff & magnet “OSEM” LOS SOS

24. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 24 Thermal 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

25. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 25 Suspension Thermal Noise G. Gonzalez, Class. Quantum Grav. 17, 4409-4435 (2000)

26. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 26 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 E 2 (r,z) (Reflected from R 1 ) z x wowo R(z) R1R1 OPL(r) E 1 (r,z) (Incident) E 2 (r,z) (Transmitted through the substrate) e wowo R(z) R1R1 OPL(r) E 1 (r,z) (Incident) (b) Mirror (a)

27. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 27 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

28. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 28 Thermal Compensation CO 2

29. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 29

30. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 30 LIGO IS Doing Astrophysics! ~2x10 -25 Upper Limits on the ellipticity of galactic pulsars Lowest ellipticity limit to date: 4.0x10 -7 for PSR J2124-3358 (f gw = 405.6Hz, distance = 0.25 kpc)

31. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 31 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

32. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 32 Enhancements to Advanced LIGO PRM Power Recycling Mirror BS Beam Splitter ITM Input Test Mass ETM End Test Mass SRM Signal Recycling Mirror PD Photodiode SILICA 40 kg 180 W 830 kW Quad Noise Prototype

33. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 33 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)

34. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 34 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

35. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 35 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 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 /2 QR

36. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 36 Interesting physical effects in Advanced LIGO Stored arm cavity power: 830 kW on resonance »Radiation pressure on resonance: F rad = 2P cav /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 F rad 40 kg LL mg

37. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 37 Optical Spring Effect For small displacements off resonance, F rad depends linearly on  L Total spring constant felt by mirror is if k tot < 0, cavity is unstable Sheard, et al., Phys. Rev. A69 051801 (2004) Solution for AdvLIGO: higher length servo gain

38. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 38 Angular Instabilities If cavity beam is displaced, F rad exerts torques on mirrors: Mirrors act as torsional pendulum »Solving equations of motions leads to one unstable mode Solution for AdvLIGO: higher alignment servo gain

39. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 39 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 modeTEM 10 mode

40. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 40 The LIGO Science Collaboration

41. Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006 41 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.orghttp://www.ligo.caltech.eduwww.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