Quantum mechanics on giant scales

1. Gravitational wavedetectors Quantum nature of light Quantum states of mirrors Quantum mechanics on giant scales Nergis Mavalvala@ GRC, March 2010

2. Outline • Quantum limit in gravitational wave detectors • Origins of the quantum limit • EM vacuum fluctuations • Interactions of light with mirrors • 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. Quantum noise in Initial LIGO Shot noise Photon counting statistics Radiation pressure noise Fluctuating photon number exerts a fluctuating force

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

7. Origin of the Quantum NoiseVacuum fluctuations

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

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

15. 10 W, frequency and intensity stabilized laser External vibrationisolation

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

17. 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

18. 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)

19. Two identical cavities with 1 gram mirrors at the ends Common-mode rejection cancels out laser noise Squeezed Vacuumfluctuations Classical noise, be vanquished

20. 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)

21. Present status

22. 18 hours Thermal noise, be vanquished! • All glass suspension • Bonded with vacseal • Glass fibers drawn in-house • Large “ears” to isolate mirror from fiber bending point • Many iterations on assembly and handling

23. 4x Present status Scattered light?

24. Heating, cooling and quanta Teff = 0.8 mKN = 35000 Wipf, Bodiya, et al. (March 2010)

25. Benchmarking with the free particle SQL

26. Quantum measurement in gravitational wave detectors

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

28. 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

29. Closing remarks

30. 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)

31. Quantum radiation pressure effects Wipf et al. (2007) Entanglement Squeezing Squeezed vacuum generation Mirror-light entanglement

32. LIGO Quantumness N = 234 SQL N = 1

33. 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