Advanced Gravitational-wave Detector Technologies

1. Advanced Gravitational-wave Detector Technologies Future generations of interferometers Nergis MavalvalaLIGO Scientific CollaborationGR-17, July 2004

2. GW interferometer 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

3. 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

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

6. The Target 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... Quantum LIGO Advanced LIGO Estimated gravity gradients Test mass thermal Suspension thermal Seismic Advanced LIGO

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. The target 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 10-19 m /Hz at 10 Hz Need 1010attenuation 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 Seismic Isolation

9. 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 Seismic Isolation Strategy 2 stage active isolation 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. 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 Mirror Suspensions

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. 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 Mechanical dissipation Thermaldisplacement spectrum Detection band Frequency internal mode pendulum mode

14. 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 Suspension thermal noise

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. 30cm Mirrors and Suspensions 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 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 number of photons a • Lower power, Pbs • Frequency dependence a response of mass to forces  Optimal input power depends on frequency

18. Initial LIGO

19. The requirement 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 Quantum LIGO Advanced LIGO Test mass thermal Suspension thermal Seismic Higher Laser Power

20. output NPRO QR f f EOM FI BP FI modemaching YAG / Nd:YAG 3x2x6 optics QR f f BP YAG / Nd:YAG / YAG HR@1064 f 2f f 3x 7x40x7 HT@808 20 W Master High Power Slave 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

21. Advanced LIGO Optics • The Challenge • 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. 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 Optical quality of mirrors

25. 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

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

27. Summarizing... • 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

29. Sub-Quantum InterferometersGeneration 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. uncorrelated 0.1 MW 1 MW 10 MW Free particle SQL

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. 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

34. Squeezing produced by back-action force of fluctuating radiation pressure on mirrors a2 b2 a1 ba f b1 Back Action Produces 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

35. Coupling coefficient k converts Da1 to Db2 • k and squeeze angle f depends on I0, fcav, losses, f a b Conventional Interferometer with Arm Cavities 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 • 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. X- X+ Sub-quantum-limited interferometer 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