Quantum Mechanics on Gigantic Scales

1. Quantum Mechanics on Gigantic Scales MIT Caltech LIGO Hanford Observatory Albert Einstein Institute Australian National University Nergis Mavalvala LHO, April 2007

2. Nature 446 (April 2007) … To stay, or to leave?That is the question… • Quantum noise in gravitational wave (GW) interferometers • Quantum states of light • Quantum behavior of giants

3. Radiationpressure noise Shot noise Quantum noise limited Advanced LIGO

4. Sub-quantum interferometers

5. Some quantum states of light • Heisenberg Uncertainty Principle for EM field • Phasor diagram analogy • Stick  dc term • Ball  fluctuations • Common states • Coherent state • Vacuum state • Amplitude squeezed state • Phase squeezed state X+ and X- associated with amplitude and phase McKenzie

6. First proposed …C.M. Caves, Phys. Rev. D 23, 1693 (1981)] Proof-of-principle … demonstration M. Xiao et al., Phys. Rev. Lett. 59, 278 (1987) More realistic configurations demonstrated … Power Recycled Michelson K. McKenzie et al., Phys. Rev. Lett. 88, 231102 (2002) Power and Signal Recycled MichelsonH. Vahlbruch et al., Phys. Rev. Lett. 95, 211102 (2005) X- X- X- X+ X- X+ X+ X+ Quantum Noise in an Interferometer Laser

7. Squeeze Source Squeezed Input Interferometer GWDetector Laser Faraday isolator Squeeze Source HomodyneDetector GW Signal

8. X- X+ Sub-quantum-limited interferometer Narrowbandunsqueezed Broadbandunsqueezed BroadbandSqueezed Quantum correlations Input squeezing

9. How to make a squeezed state? • Correlate the ‘amplitude’ and ‘phase’ quadratures • Correlations  noise reduction • Correlate quadratures through a nonlinear coupling process • Intensity-dependent refractive index in a nonlinear crystal couples amplitude and phase • Radiation pressure (amplitude) induced motion of a mirror couples to phase shift of light in a cavity

10. Squeezed state generation using nonlinear optical materials

11. Nonlinear optical media a a b b a a Parametric oscillation Second harmonic generation a The output photon quadratures are correlated a a b a Parametric amplification

12. Optical Parametric Oscillator SHG

13. Squeezing measured… Goda et al., submitted to Opt. Lett. (2007) Vahlbruch et al., PRL 97, 011101 (2007)

14. Squeezing injected @ the 40m prototype @ Caltech Goda et al. (2007)

15. Squeezed state generation using radiation pressure ↔ mechanical oscillator coupling

16. Radiation-oscillator coupling Amplitude-phase correlations 1. Light with amplitude fluctuations DA incident on mirror Movable mirror 2. Radiation pressure due to DA causes mirror to move by Dx 3. Phase of reflected lightDf depends on mirror position and hence light amplitude, i.e DADx  Df

17. Ponderomotive predominance • An experimental apparatus in which radiation pressure forces dominate over mechanical forces • Ultimate goals • Generation of squeezed states of light • Quantum ground state of the gram-scale mirror • Mirror-light entanglement • En route • Optical cooling and trapping • Diamonds • Parametric instabilities • Disclaimer • Any similarity to a gravitational wave interferometer is not merely coincidental. The name and appearance of lasers, mirrors, suspensions, sensors have been changed to protect the innocent.

18. Key ingredients Low mass, low noise mechanical oscillator mirror – 1 gm with 1 Hz resonant frequency High circulating power – 10 kW High finesse cavities10000 Differential measurement – common-mode rejection to cancel classical noise Optical spring – noise suppression and frequency independent squeezing A “ponderomotive” squeezing source

19. Assumed experimental parameters T. Corbitt et al., Phys. Rev A 73, 023801 (2006)

20. Noise budget T. Corbitt et al., Phys. Rev A 73, 023801 (2006)

21. Cooling and trapping

22. Cooling and Trapping Two forces are useful for reducing the motion of a particle • A restoring force that brings the particle back to equilibrium if it tries to move • Position-dependent force  SPRING • A damping force that reduces the amplitude of oscillatory motion • Velocity-dependent force  VISCOUS DAMPING TRAPPING COOLING

23. Mechanical forces • Mechanical forces come with thermal noise • Stiffer spring (Wm↑)  larger thermal noise • More damping (Qm↓)  larger thermal noise

24. Optical forces • Optical forces do not introduce thermal noise • Laser cooling • Reduce the velocity spread Velocity-dependent viscous damping force • Optical trapping • Confine spatiallyPosition-dependent optical spring force

25. Cooling and trapping • A whole host of tricks for atoms and ions (or a few million of them) • Magneto-Optic Traps (MOTs) • Optical molasses • Doppler cooling • Sisyphus cooling (optical pumping) • Sub-recoil limit • Velocity-selective coherent population trapping • Raman cooling • Evaporative cooling

26. 1997 Nobel Prize in Physics Steven Chu, Claude Cohen-Tannoudji and William D. Phillipsfor their developments of methods to cool and trap atoms with laserlight This year's Nobel laureates in physics have developed methods of cooling and trapping atoms by using laser light. Their research is helping us to study fundamental phenomena and measure important physical quantities with unprecedented precision.

27. 2004 What about bigger things? • Cavity cooling (cold damping) • Use the time delay of light stored in an optical cavity to produce a velocity-dependent viscous damping force • Nano- and micro-mechanical oscillators • Trapping requires a position-dependent force • Use the position-dependence of the intensity in an optical cavity  OPTICAL SPRING • Gram-scale objects

28. Detune a resonant cavity to higher frequency (blueshift) Opposite detuning than cold damping 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

29. Stable optical springs • Optical springs are always unstable if optical forces dominate over mechanical ones • Can be stabilized by feedback forces • Key idea: The optical damping depends on the response time of the cavity, but the optical spring does not So use two fields with a different response time • Fast response creates restoring force and small anti-damping • Slow response creates damping force and small anti-restoring force • Can do this with two cavities with different lengths or finesses • But two optical fields with different detunings in a single cavity is easier

30. Experiments

31. Phase II cavity 10% 90% 5 W

33. Double suspension for mini mirror

34. Steel shell of same diameter as LIGO auxiliary optics • Suspended with magnets (actuation), standoffs (thermal noise) • Mini mirror attached by two 300 micron fused silica fibers Little mirror suspension

35. 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 • Independently control spring constant and damping T. Corbitt et al., PRL (2007)

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) Diamonds? 5 kHz K = 2 x 106 N/mCavity optical mode  diamond rod Displacement / Force Frequency (Hz)

37. Optical cooling T. Corbitt et al., PRL (2007) Increasing subcarrier detuning

38. Lower frequency mechanical resonance  13 Hz Shorter cavity (0.1 m)  less frequency noise Some acoustic features (beam clipping?) Electronic damping Cooler mirror T. Corbitt et al., to be submitted (2007)

39. Approaching a quantum state • Ponderomotive experiment with two cavities • Without optical trapping • With optical trap at 1 kHz

40. What’s next…

41. In principle… • Present limit from laser frequency and VCO noise • Expect 1000x suppression of this with second cavity (going on now) • Output light squeezing • Suspension and coating thermal noise low enough? • Optical losses low enough? • Cooling • Temperature drops as noise2 expect to get to mK • Within factor of 10 to 100 of occupation number = 1 • Prospect of seeing quantum behavior of an object with 1022 atoms by coupling it to an optical field with 1015 photons

43. Hole for transmitted light OSEM assemblies Optical Sensor EM actuator for 0.25 kg input mirror (roughly to scale) 5 OSEMs in less space than a single LIGO OSEM Earthquake stop

44. 25 micron music wire. Actual wire to be usedis 5 micron tungsten.

45. Lessons learned so far…

46. Parametric instability Acoustic drumhead modes (28 kHz, 45 kHz, 75 kHz, …) become unstable when detuned at high power • Viscous radiation pressure drives mode  parametric instability • Detuning in opposite direction reduces Q of the mode  cold damping • Mode stabilized through feedback to laser frequency Parametric instability (restoring force) Cold damping (anti-restoring force) T. Corbitt et al., Phys. Rev A 74, 021802R (2006)

47. Control system challenges • Digital control system (32 kS/sec) • Optical spring changes mechanical dynamics of mirrors  servo design • Parametric instabilities for modes at tens of kHz • Analog control forces applied directly on mirrors via magnet-coil pairs • Control system strong enough to maintain cavity resonance but not interfere with radiation pressure induced motion • Large power buildup • Large dynamic range • Transients

48. Between 100 and 1000 Hz GAIN < 1 System behaves freely Important for observing squeezing Optical spring requires major reshaping of electronic servo compensation Control system Loop gain No optical spring Measured data With optical spring

49. In closing... • Prospects for a sub-quantum-noise-limited GW interferometer look good in coming years • Spin offs in precision measurement and quantum physics

50. Thanks to National Science FoundationLIGO Laboratory and Collaboration