The Quantum Limit and Beyond in Gravitational Wave Detectors

1. Gravitational wavedetectors Quantum nature of light Quantum states of mirrors The Quantum Limit and Beyond in Gravitational Wave Detectors Nergis MavalvalaAPS, April 2009

2. Outline • Quantum limit for gravitational wave detectors • Origins of the quantum limit • Vacuum fluctuations of the EM field • Quantum states of light • Squeezed state injection and generation • Quantum states of the mirrors • Radiation pressure induced dynamics • Prospects for observing quantum effects in macroscopic objects (mirrors)

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

4. Shot noise More laser power  stronger measurement Radiation pressure noise Stronger measurement  larger backaction Advanced LIGO Quantum noise everywhere

5. Origin of the Quantum NoiseVacuum fluctuations

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

7. 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 Radiation pressure noise Quantum fluctuations exert fluctuating force  mirror displacement 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) Laser

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

9. Advanced LIGO with squeeze injection Radiation pressure Shot noise

10. Desired properties of squeezed states for GW detectors • Squeezing in the GW band(10 Hz to 10 kHz) • Large squeezing factors(e.g. 10 dB  factor of 3 improvement in strain sensitivity) • Compatibility with other noise sources(“Do no harm” in GW band) • Stable long term operation of squeezer • Frequency-dependent squeezing

11. Squeezed state generation

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

13. 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

14. The sum of correlated upper and lower quantum sidebands  a squeezed state Squeezing with optical nonlinearity

15. Squeezing using nonlinear optical media

16. Basic principle a a b b a a Parametric oscillation Second harmonic generation a The output photon quadratures are correlated a a b a Parametric amplification

17. Vacuum (shot) Noise power (dBm/rtHz) Squeezed Dark Frequency (Hz) Vahlbruch et al., New Journal of Physics 9, 371(2007) 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

18. Squeezing injection 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

19. Noise power (dBm) Frequency (MHz) Vahlbruch et al., Phys.Rev.Lett.95, 211102 (2005) Frequency-dependent 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 OPA Faraday rotator ASPD Filter cavities SHG

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

21. Squeeze injection in a suspended-mirror interferometer: 40m prototye (Caltech)

22. Measurement of squeezingBalanced Homodyne Detection SQZ LO

23. Quantum enhancement at 40m 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)

24. Crystal squeezing experiments Progress in last ~half decade • Squeezing at audio frequencies • Filter cavities for frequency-dependent squeezing • Detailed calculations of noise couplings to establish fundamental limits • Coherently controlled squeezing  long term operation • 10 dB of available squeezing • GW interferometers 6 dB at frequencies > 10 Hz, 11 dB at MHz Suspended interferometer test at 40m

25. Design squeezing source for injection into Advanced LIGO Possible test of low-noise, low-frequency performance in Enhanced LIGO Squeezing Enhancement in LIGO

26. Improve high frequency sensitivity Expect to install in summer 2009 Squeezing Enhancement in GEOHF

27. Radiation pressurethe other quantum noise

28. Optical spring Optical damping Radiation pressure rules! • Experiments in which radiation pressure forces dominate over mechanical forces • Classical light-oscillator coupling effects(dynamical backaction) • Optical cooling and trappingof mirrors • Opportunity to study quantum effects in macroscopic systems • Observation of quantum radiation pressure • Generation of squeezed states of light • Entanglement of mirror and light quantum states • Quantum ground state of (kilo)gram-scale mirrors

29. Optically trapped and cooled mirror Optical fibers Teff = 6.9 mKN = 105 1 grammirror T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett 99, 160801 (2007)

30. MIT Keisuke Goda Thomas Corbitt Christopher Wipf Timothy Bodiya Sheila Dwyer Nicolas Smith Eugeniy Mikhailov Edith Innerhofer MIT LIGO Lab NSF Collaborators Roman Schnabel and group Henning Vahlbruch Yanbei Chen and group Helge Müller-Ebhardt Henning Rehbein Stan Whitcomb Daniel Sigg Rolf Bork Alex Ivanov Jay Heefner Caltech 40m Lab David McClelland and group Kirk McKenzie Ping Koy Lam LIGO Scientific Collaboration Cast of characters

31. GWDetector Laser The End Faraday isolator SHG OPO HomodyneDetector Squeeze Source GW Signal

32. Supplementary info

33. Quantum states of light • Classical light • Quantum optics

34. The sum of correlated upper and lower quantum sidebands  a squeezed state Squeezing with optical nonlinearity

35. High Level of Squeezing & Long-Term Stability • High nonlinearity • LiNbO3 vs PPKTP • Low optical losses • Use supermirrors • High pump power • 1 W or higher • Thermally stable • Wider phase-matching temperature range PPKTP (KTiOPO4) Crystal

36. Second-Harmonic Generator (SHG) • SHG conversion efficiency = 30% • The second-harmonic field pumps the OPO cavity

37. Optical Parametric Oscillator (OPO) • High power (few 100 mW) green pump field in OPO correlates upper and lower quantum sidebands around carrier  squeezing Output Coupler Input Coupler PPKTPCrystal

38. Measurement Balanced Homodyne Detection SQZ LO

39. Vacuum (shot) Noise power (dBm/rtHz) Squeezed Dark Frequency (Hz) Vahlbruch et al. (2007) Audio frequency squeezing

40. Frequency dependent squeezing Vahlbruch et al., Phys.Rev.Lett.95, 211102 (2005)

41. Noise power (dBm) Frequency (MHz) Vahlbruch et al., Phys.Rev.Lett.95, 211102 (2005) Frequency-dependent squeezing

42. Frequency-dependence with state tomography

43. Frequency-dependence with state tomography