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Ultracold mirrors

Ultracold mirrors. MIT Corbitt, Ackley, Bodiya, Ottaway, Smith, Wipf. Caltech Bork, Chen, Heefner, Sigg, Whitcomb. Nergis Mavalvala Springer Forum, Sept. 2008. AEI Ebhardt-Mueller, Rehbein. Putting “MECHANICS” back into quantum mechanics. K. Schwab. A quantum mechanical oscillator.

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Ultracold mirrors

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  1. Ultracold mirrors MITCorbitt, Ackley, Bodiya, Ottaway, Smith, Wipf CaltechBork, Chen, Heefner, Sigg, Whitcomb Nergis MavalvalaSpringer Forum, Sept. 2008 AEIEbhardt-Mueller, Rehbein

  2. Putting “MECHANICS” back into quantum mechanics K. Schwab

  3. A quantum mechanical oscillator • Quantum mechanics 1 • Particle in a harmonic potential well with simple and familiar Hamiltonian • This mechanical oscillator seems such a tangible quantum device • But there is no experimental system as yet that requires a quantum description for a macroscopic mechanical oscillator • Useful for making very sensitive position or force measurements • Gravitational wave detectors • Atomic force microscopes

  4. 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

  5. Reaching the quantum limit in mechanical oscillators • 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

  6. 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

  7. 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 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

  8. Optical trapping of mirrors

  9. 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?

  10. 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

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

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

  13. Vacuum chamber – MIT LIGO Lab

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

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

  16. 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)

  17. Supercold mirrors Toward observing mirror quantum states

  18. 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., PRL (2007)

  19. 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)

  20. 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)

  21. Quantum measurement in a gravitational wave detector

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 200x 1012x Cavity cooling

  28. Summary

  29. 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)

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

  31. Initial LIGO Quantumness 1.4 mK SQL

  32. In conclusion • MIT experiments in the extreme radiation pressure dominated regime have yielded 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

  33. 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

  34. The End

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