Confronting Quantum Limits in Gravitational Wave Detectors

1. Gravitational wavedetectors Quantum nature of light Quantum states of mirrors Confronting Quantum Limits in Gravitational Wave Detectors Nergis Mavalvala@ DFS, June 2010

2. Outline • Gravitational wave 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 • My story

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 LCGT AIGO LIGO LISA

6. 3 0 3 ( ± 0 1 k 0 m m s ) LIGO: Laser Interferometer Gravitational-wave Observatory WA MIT 4 km NSF Caltech LA 4 km http://ligo.mit.edu

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

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

9. Origin of the Quantum NoiseVacuum fluctuations

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

11. 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

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

13. Advanced LIGO with squeeze injection Radiation pressure Shot noise

14. Squeezed State Generation

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

16. 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

17. Squeezed state generation Anti-squeezed Vacuum (shot) Noise power (dBm) Squeezed Frequency (Hz) Time (s) Vahlbruch et al., PRL (2008) Goda et al., Opt. Lett. (2008)

18. Quantum EnhancementSqueezed state injection

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

20. 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

21. Squeezed state injection has arrived! • Implementation in GEO600 • Installed, in commissioning phase • Implementation in a 4km LIGO detector • Under construction • Installation and commissioning at LIGO Hanford begins 4Q 2010 • A direct application of quantum metrology

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

23. 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

24. Radiation pressure:Another way to squeeze light • Create correlations between light quadratures using a movable mirror • Amplitude fluctuations of light impart fluctuating momentum to the mirror • Mirror displacement is imprinted on the phase of the light reflected from it

25. Radiation pressure:Another way to squeeze light • Create correlations between light quadratures using a movable mirror • Amplitude fluctuations of light impart fluctuating momentum to the mirror • Mirror displacement is imprinted on the phase of the light reflected from it

26. Two identical cavities with movable mirrors Common-mode rejection cancels out laser noise Squeezed Vacuumfluctuations Intra-interferometer squeezing

27. 7 dB or 2.25x Squeezing Squeezing T. Corbitt, Y. Chen, F. Khalili, D.Ottaway, S.Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev A 73, 023801 (2006)

28. Classical building blocks

29. 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

30. 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

31. The optical spring effect and optical trapping of mirrors

32. Optical cavities • Light storage device • Two mirrors facing each other • Interference  standing wave Intracavity power Cavity length or laser wavelength

33. Detune a resonant cavity to higher frequency (blueshift) Change in cavity mirror position changes intracavity power Change in radiation-pressure exerts a restoring force on mirror Time delay in cavity response introduces a viscous anti-damping force x P How to make an optical spring?Radiation pressure force

34. 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

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

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

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

38. 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)

39. Quantum measurement in gravitational wave detectors

40. 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

41. 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

42. Closing remarks

43. 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)

44. Quantum radiation pressure effects Squeezing Teff = 0.8 mKN = 35000 Squeezed vacuum generation Present status

45. LIGO Quantumness N = 234 SQL N = 1

46. And finally…

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

48. My story • Born and raised in Pakistan • Attended “export” high school in Karachi • Undergraduate degree from Wellesley College in the US • Doctorate from MIT in 1997 • Postdoc at Caltech • Junior faculty at MIT (2002 to 2009) • Parent to baby Evren (2008) • Full professor at MIT (2009 – )

49. International Conference on Women in Physics • Seoul, Korea 2008 • Stellenbosch, South Africa, April 2011

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