Quantum mechanics on giant scales

1. Gravitational wavedetectors Quantum nature of light Quantum states of mirrors Quantum mechanics on giant scales Nergis MavalvalaMIT, September 2008

2. Outline • Quantum limit for gravitational wave detectors • Origins of the quantum limit • Vacuum fluctuations • Interactions of light with mirrors • Quantum states of light • Squeezed state injection and generation • Quantum states of the mirrors • Observing quantum effects in macroscopic objects • Burgeoning field of macroscopic quantum measurement

3. Laser Laser Photodetector Photodetector GW from space Want very large L Basics of GW Detection • Gravitational Waves “Ripples in space-time” • Stretch and squeeze the space transverse to direction of propagation

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

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

6. The Standard Quantum Limit

7. Advanced LIGO Quantum noise everywhere

8. Origin of the Quantum NoiseVacuum fluctuations

9. 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 X1 and X2 associated with amplitude and phase

10. 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) Laser

11. Quantum EnhancementSqueezed state injection

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

13. How to squeeze? • But with photons… • 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. Squeezing injection in Advanced LIGO Prototype GW detector Laser SHG Faraday isolator OPO HomodyneDetector Squeeze Source GW Signal

15. Quantum enhancement 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)

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

17. Advanced LIGO with squeeze injection Radiation pressure Shot noise

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

19. Radiation pressure rules! • Experiments in which radiation pressure forces dominate over mechanical forces • Study radiation pressure effects on large masses to inform future GW detectors • Major spin-offs – opportunity to study quantum effects in macroscopic systems • Observation of quantum radiation pressure • Generation of squeezed states of light • Quantum state of the gram-scale mirror • Entanglement of mirror and light quantum states • Classical light-oscillator coupling effects en route • Optical cooling and trapping • Light is stiffer than diamond

20. Quantum mechanics of macroscopic oscillators • Quantum control of light and matter  noise reduction techniques • Precision measurements of forces and displacements • Explore the quantum-classical boundary • Ground state cooling • Direct observation of quantum effects • Superpositions • Entanglement • Decoherence • Quantum backaction evading measurements

21. Key ingredients Two identical cavities with 1 gram mirrors at the ends High circulating laser power Common-mode rejection cancels out laser noise Optical spring effect to suppress external force (thermal) noise A radiation pressure dominated interferometer

22. The optical spring effect and optical trapping of mirrors

23. 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

24. 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 True for any non-mechanical force ( non-dissipative or “cold” force),e.g. gravitation, electronic, magnetic Connect a high Q, low stiffness mechanical oscillator to a stiff optical spring  DILUTION

25. 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?

26. Detune a resonant cavity to higher frequency (blueshift) Real component of optical force  restoring But imaginary component (cavity time delay)  anti-damping Unstable Stabilize with feedback Anti-restoring Restoring Anti-damping Damping Optical springs and damping Cavity cooling

27. Observable quantum effects

28. Radiation pressureAnother way to squeeze… • 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

29. Radiation pressureAnother way to squeeze… • 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

30. 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)

31. Correlate two optical fields by coupling to mechanical oscillator Quantum state of each light field not separable (determined by measuring density matrix) Quantify the degree of non-separability using logarithmic negativity Entanglement Entanglement C. Wipf, T. Corbitt, Y. Chen, and N. Mavalvala, New J. Phys./283659 (2008)

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

33. Experimental layout 10% 90% 5 W 1 m

34. Seismically isolated optical table Experimental Platform Vacuum chamber 10 W, frequency and intensity stabilized laser External vibrationisolation

35. Mechanical oscillator Optical fibers 1 grammirror Coil/magnet pairs for actuation(x5)‏

36. How stiff is it? 100 kg person  Fgrav ~ 1,000 N  x = F / k = 0.5 mm Very stiff, but also very easy to break Maximum force it can withstand is only ~ 100 μN or ~1% of the gravitational force on the 1 gm mirror Replace the optical mode with a cylindrical beam of same radius (0.7mm) and length (0.92 m)  Young's modulus E = KL/A Cavity mode 1.2 TPa Compare to Steel ~0.16 Tpa Diamond ~1 TPa Single walled carbon nanotube ~1 TPa (fuzzy) Extreme optical stiffness 5 kHz K = 2 x 106 N/mCavity optical mode  diamond rod Displacement / Force Phase increases  unstable Frequency (Hz)

37. Double optical spring  stable optical trap • Two optical beams  double optical spring • Carrier detuned to give restoring force • Subcarrier detuned to other side of resonance to give damping force with Pc/Psc = 20 • Independently control spring constant and damping Stable! T. Corbitt et al., Phys. Rev. Lett 98, 150802 (2007)

38. Supercold mirrors Toward observing mirror quantum states

39. Optical cooling with double optical spring(all-optical trap for 1 gm mirror) Increasing subcarrier detuning T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf and N. Mavalvala, Phys. Rev. Lett 98, 150802 (2007)

40. 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)

41. Present status

42. Even bigger mirror, even cooler • Meanwhile, Initial LIGO detectors much more sensitive  operate at 10x above the standard quantum limit • But these interferometers don’t have strong radiation pressure effects  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

43. Quantum measurement in Initial LIGO

44. 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

45. Some other cool oscillators Toroidal microcavity 10-11 g NEMS  10-12 g AFM cantilevers 10-8 g Micromirrors 10-7 g SiN3 membrane  10-8 g LIGO  103 g Minimirror  1 g

46. 200x 1012x Cavity cooling

47. Closing remarks

48. In conclusion • MIT experiments in the extreme radiation pressure dominated regime have yielded several important classical results • Extreme optical stiffness  few MegaNewton/m • Stiff and stable optical spring  optical trapping of mirrors • Optical cooling of 1 gram mirror  few milliKelvin • Established path toward quantum regime where we expect to observe radiation pressure induced squeezed light, entanglement and quantum states of very macroscopic objects

49. In conclusion • Initial LIGO completed a scientific data taking run at design sensitivity in 2007 • An intermediate-scale upgrade – Enhanced LIGO – is currently being commissioned • Advanced LIGO is funded and commissioning is expected to start in 2011 • Quantum noise is a significant limitation in these detectors • Application of quantum optics techniques to improve LIGO detector sensitivity • Squeezed state generation and injection is a mature technique and poised to be deployed in the LIGO detectors in the near future

50. In conclusion • LIGO detectors operate close to the standard quantum limit • An excellent testbed for observing quantum behavior in macroscopic objects • Feedback cooling in Initial LIGO interferometers achieved occupation number N ~ 200 • Present upgrade (Enhanced LIGO, 2010) should have N ~ 50 • Advanced LIGO (2015) should operate at the Standard Quantum Limit and lead to N ~1 • Will also detect gravitational waves