Quantum mechanics on giant scales

1. Quantum mechanics on giant scales MITCorbitt, Ackley, Bodiya, Ottaway, Smith, Wipf CaltechBork, Chen, Heefner, Sigg, Whitcomb Nergis MavalvalaDAMOP, May 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 is the most 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. 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

5. 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

6. An all-optical trap

7. 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 • Ultimate goals • Observation of quantum radiation pressure • Generation of squeezed states of light • Quantum state of the gram-scale mirror • Entanglement • Classical light-oscillator coupling effects en route • Optical cooling and trapping • Diamonds

8. 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

9. Experiments Extreme optical stiffness Stable optical trap Optically cooled mirror

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

11. Vacuum chamber – MIT LIGO Lab

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

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

14. 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)

15. 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)

16. Optical cooling with double optical spring(all-optical trap for 1 gm mirror) T. Corbitt et al., PRL (2007) Increasing subcarrier detuning

17. 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 Mechanical Q = 20000Cooling factor = 43000 Only cooling result to date where cooling factor exceeded the mechanical Q Optical spring with active feedback cooling T. Corbitt et al., PRL (2007)

18. Even bigger mirror, even cooler • Working on reduction of excess noise in radiation pressure experiment at present • Meanwhile, current LIGO detectors are much more sensitive  operate at 10x above the standard quantum limit • LIGO just completed a two year science data taking run  opportunity! • But these interferometers don’t have strong radiation pressure effects  no optical spring or damping • Introduce a different kind of cold spring  restoring force from electronic feedback

19. Quantum measurement in Initial LIGO

20. Kilogram-scale mirrors (LIGO)‏ 25 cm diameter 10 cm thick M ~ 10.8 kg ~ 1026 atoms Wosc = 2 p x 0.7 Hz

21. Most sensitive degree of freedom is differential arm motion Reduced mass is ¼ x 10.8 kg = 2.7 kg Since optical force is insufficient, use electronic feedback to generate both spring and damping forces Cold damping ↔ cavity cooling Servo spring ↔ optical spring cooling LIGO interferometers

22. Measurement performed at LIGO Hanford Observatory Controller comprised a restoring force and a variable damping force Choose 150 Hz as most sensitive measurement band Measure response of servo spring for various damping gains Deviations from perfect spring due to various filters for low frequency gain and high frequency cutoffs Servo spring

23. Lowest effective temperature = 1.4 mK Cooling factor 2 x 108 below room temperature Lowest occupation number = 234 Limited primarily by shot noise Conservative estimate of center of mass motion Uncertainty in limiting noise source leads to overestimate of COM motion Initial LIGO Cooling LIGO Scientific Collaboration, submitted to Nature (2008)

24. Some other cool oscillators SiN3 membranes  10-11 g NEMS  10-12 g AFM cantilevers 10-8 g Micromirrors 10-7 g Toroidal microcavities 10-12 g LIGO  103 g Minimirror  1 g

25. 200x 1012x Cavity cooling

26. Summary

27. 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)

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

29. Initial LIGO Quantumness 1.4 mK SQL

30. In conclusion • Classical radiation pressure effects observed and characterized in system with 1 gram mirror • Extreme optical stiffness • Free and stable optical spring • Optical trapping technique that could lead to direct measurement of quantum behavior of a 1 gram object • Parametric instabilities (photon-phonon coupling) • Control system interaction • Testing extremely high power densities on small mirrors (20 kW in cavity  1 MW/cm2) • Nothing has blown up or melted (yet) • Established path to observing radiation pressure induced squeezed light, entanglement and quantum states of truly macroscopic objects

31. In conclusion • 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 (with an optical spring instead of a servo spring)

32. The End

33. 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 TRAPPINGConfine spatially COOLINGReduce velocity spread

34. Cooling (Teff – T0) Γ0 + (Teff – T1)Γ1 = 0 Teff = (T1Γ1 + T0 Γ0) / (Γ0 + Γ1)‏ Teff ≈ T0 Γ0/ Γ1 Γ = damping rate Ω = resonant frequency Γ0 Ω0 Environment T0 Mass Teff Cooling factor limited by Ω0 / Γ0 Γ1 (>>Γ0 ) Gravitational, optical, electronic, magnetic... T1(<< T0)‏

35. Dilution Γ = damping rate Ω = resonant frequency Cooling factor limited by Ω1 / Γ0 Maximize Ω1 Minimize Ω0 , Γ0 Γ0 Ω0 Environment T0 Mass Teff Γ1 Ω1(>>Ω0) Use second spring to stiffen and cool system Gravitational, optical, electronic, magnetic... T1(<< T0)‏

36. A note about calibration Sensor noise What we want to measure + + Mirror Force noise Mirror Position Controller What we measure For each frequency band, we assume the worst case scenario for force or sensor noise in order to estimate the real mirror motion

37. 104x 1011x Cavity cooling efforts

38. March toward the quantum world…

39. Squeezed light Correlate amplitude and phase quadratures of light by coupling to mechanical oscillator Achieve noise level lower than shot noise limit for either amplitude or phase quadrature Entanglement Correlate two optical fields by coupling to mechanical oscillator Quantum state of each light field not separable (determined by measuring density matrix) Observation of quantum effects Creating quantum correlations

40. Interferometer configuration

41. 7 dB Squeezing T. Corbitt et al., Phys. Rev A 73, 023801 (2006)

42. Light entanglement • Logarithmic negativity • Measure of continuous variable entanglement • Degree to which density matrices of C and SC are not separable • Calculated using quantum Langevin approach Cavity linewidth Optical spring resonance Entanglement(also squeezing) C. Wipf et al. PRL (2008)