Interferometric Gravitational Wave Detectors: Giant Quantum Machines

1. Interferometric Gravitational Wave Detectors:Giant Quantum Machines Nergis Mavalvala Department of Physics Massachusetts Institute of Technology Pracqsys 2010, June 2010

2. Outline • Gravitational waves • Interferometric detectors • Next generation detectors and the quantum limit • Getting past the quantum limit • Experiments • Quantum optics • Quantum optomechanics • Necessary building blocks in the classical regime • Progress toward the quantum regime

3.  Gravitational waves (GWs) • Prediction of Einstein’s General Relativity (1916) • Indirect detection led to Nobel prize in 1993 • Ripples of the space-time fabric • GWs stretch and squeeze the space transverse to direction of propagation • Emitted by accelerating massive objects • Cosmic explosions • Compact stars orbiting each other • Stars gobbling up stars • “Mountains” on stellar crusts

4. GW detector at a glance • Mirrors hang as pendulums • Quasi-free particles • Respond to passing GW • Filter external force noise 4 km 20 kW • Optical cavities • Mirrors facing each other • Builds up light power • Lots of laser power P • Signal P • Noise  10 W

5. Global network of detectors GEO VIRGO LIGO TAMA AIGO LIGO LISA

6. Quantum noise in Initial LIGO Shot noise Photon counting statistics Radiation pressure noise Fluctuating photon number exerts a fluctuating force

7. LIGO listened…And had something to say

8. The search for GRB070201 • GRB 070201 • Very luminous short duration, hard gamma-ray burst • Detected by Swift, Integral, others • Consistent with being in M31 • Leading model for short GRBs: binary merger involving aneutron star • Looked for a GW signal in LIGO • No plausible GW signal found • Can say with >99% confidence that GRB070201 was NOT caused by a compact binary star merger in M31 • Conclusion: it was most likely a Soft Gamma Repeater giant flare in M31 25% 50% 75% 90% DM31 • Abbott et al., Ap. J 681, 1419 (2008) • Mazets et al., Ap. J 680, 545 (2008) • Ofek et al., Ap. J 681, 1464 (2008)

9. Farther away

10. Shot noise More laser power  stronger measurement Radiation pressure noise Stronger measurement  larger backaction Strain sensitivity

11. Origin of the Quantum NoiseVacuum fluctuations

12. X2 X1 X2 Shot noise limited  (number of photons)1/2 Arbitrarily below shot noise X1 X2 X2 Vacuum fluctuations Squeezed vacuum X1 X1 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) Goda et al., Nature Physics (2008) Radiation pressure noise Quantum fluctuations exert fluctuating force  mirror displacement Laser

13. Quantum EnhancementSqueezed state injection

14. Squeezing injection in Advanced LIGO GWDetector Laser SHG Faraday isolator Squeezing source OPO HomodyneDetector Squeeze Source GW Signal

15. Advanced LIGO with squeeze injection Radiation pressure Shot noise

16. Squeezed State Generation

17. How to squeeze? • My favorite way • A tight hug

18. 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

19. Typical squeezer apparatus Second harmonic generator (SHG) • Convert 1064 nm  532 nm with ~50% efficiency Optical parametric oscillator (OPO) • Few 100 mW pump field (532 nm) correlates upper and lower quantum sidebands around carrier (1064 nm)  squeezing Balanced homodyne detector • Beat local oscillator at 1064nm with squeezed field Laser IFO OPO Faraday rotator ASPD SHG

20. Vahlbruch et al,. PRL 2008 Squeezing in GW (audio) band

21. Squeezing injection in 40m prototype Prototype GW detector Laser SHG Faraday isolator OPO HomodyneDetector Squeeze Source Diff. mode signal

22. 2.9 dB or 1.4x 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) Squeezing injectionin a prototype interferometer

23. Squeezed state injection has arrived! • Implementation in GEO600 • Installed, commissioning phase • Implementation in a 4km LIGO detector • Under construction, installation and commissioning begin 4Q 2010 • A direct application of quantum metrology

24. Radiation pressure The other side of the quantum optical coin

25. Radiation pressure rules! • Experiments in which radiation pressure forces dominate over mechanical forces • Opportunity to study quantum effects in macroscopic systems • Observation of quantum radiation pressure • Generation of squeezed states of light • Quantum ground state of the gram-scale mirror • Entanglement of mirror and light quantum states • Classical light-oscillator coupling effects en route(dynamical backaction) • Optical cooling and trapping • Light is stiffer than diamond

26. Reaching the quantum limit in mechanical oscillators • The goal is to measure non-classical effects with large objects like the (kilo)gram-scale mirrors • The main challenge  thermally driven mechanical fluctuations • Need to freeze out thermal fluctuationsZero-point fluctuations remain • One measure of quantumness is the thermal occupation number • Want N  1 Colder oscillator Stiffer oscillator

27. True for any non-mechanical force ( non-dissipative or “cold” force ), e.g. gravitation, electronic, magnetic Mechanical vs. optical forces • Mechanical forces  thermal noise • Stiffer spring (Wm↑)  larger thermal noise • More damping (Qm↓)  larger thermal noise • Optical forces do not affect thermal noise spectrum Fluctuation-dissipation theorem Connect a high Q, low stiffness mechanical oscillator to a stiff optical spring  DILUTION

28. The optical spring effect and optical trapping of mirrors

29. Radiation pressure of light in an optical cavity  force on mirror Detune a resonant cavity to higher frequency (blueshift) Real component of optical force  restoring But imaginary component (cavity time delay)  anti-damping Unstable Can stabilize with feedback Anti-restoring Restoring Anti-damping Damping Optical springs and damping Optical spring Cavity cooling

30. Classical Experiments Extreme optical stiffness Stable optical trap Optically cooled mirror

31. Experimental cavity setup 1 m 10% 90% 5 W Optical fibers 1 grammirror Coil/magnet pairs for actuation (x5)‏

32. 10 W, frequency and intensity stabilized laser External vibrationisolation

33. Dynamic backaction cooling Stable optical trap with two colors Trapping and cooling Stiff! Stable! T. Corbitt et al., Phys. Rev. Lett 98, 150802 (2007)

34. Active feedback cooling • Measure mirror displacement • Filter displacement signal • Feed it back to mirror as a force Controller PDH Laser EOM PBS QWP • Continuous measurement  measurement-induced decoherence

35. Experimental improvements Reduce mechanical resonance frequency (from 172 Hz to 13 Hz) Reduce frequency noise by shortening cavity (from 1m to 0.1 m) Electronic feedback cooling instead of all optical Cooling factor = 43000 Optical spring with active feedback cooling Teff = 6.9 mKN = 105 T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett 99, 160801 (2007)

36. Quantum measurement in gravitational wave detectors

37. Initial LIGO detectors much more sensitive  operate at 10x above the standard quantum limit But these interferometers don’t have strong radiation pressure effects (yet)  no optical spring or damping Introduce a different kind of cold spring  use electronic feedback to generate both restoring and damping forces Cold damping ↔ cavity cooling Servo spring ↔ optical spring cooling Even bigger, even cooler SQL

38. Active feedback cooling + spring • Measure mirror displacement • Filter displacement signal • Feed it back to mirror as a force Controller PDH Laser EOM PBS QWP

39. Cooling the kilogram-scale mirrors of Initial LIGO Teff = 1.4 mKN = 234T0/Teff = 2 x 108 Mr ~ 2.7 kg ~ 1026 atoms Wosc = 2 p x 0.7 Hz LIGO Scientific Collaboration

40. Closing remarks

41. Classical radiation pressure effects Stiffer than diamond 6.9 mK Stable OS Radiation pressure dynamics Optical cooling 10% 90% 5 W ~0.1 to 1 m Corbitt et al. (2007)

42. Quantum radiation pressure effects Squeezing Squeezed vacuum generation Present status

43. LIGO Quantumness N = 234 SQL N = 1

44. And now for the most important part…

45. MIT Thomas Corbitt Christopher Wipf Timothy Bodiya Sheila Dwyer Nicolas Smith Eric Oelker MIT LIGO Lab Collaborators Yanbei Chen and group Stan Whitcomb Daniel Sigg Rolf Bork Alex Ivanov Jay Heefner LIGO Scientific Collaboration Cast of characters

46. Gravitational wavedetectors Quantum nature of light Quantum states of mirrors The End