1. Quantum mechanics on giant scales
Quantum nature of light
Quantum states of mirrors
Nergis Ithaca College, December 2008

2. Quantum vs. Classical World
Quantum theory was proposed to explain the microscopic world of atoms
Classical mechanics
Exact measurement  particles located at a single, well-defined position
Continuous energy levels
Quantum mechanics
Intrinsic uncertainty in measurement  particles has probability of being somewhere
Discrete energy levels

3. A quantum mechanical oscillator
Quantum mechanics 1
Particle in a harmonic potential well with simple and familiar Hamiltonian
But there is no experimental system as yet that requires a quantum description for a macroscopic mechanical oscillator
Potential energy of form kx2
Energy
En = (n+½) ħω
n = 3
n = 2
n = 1
n = 0
E0 = ½ħω x

4. Macroscopic oscillators in the quantum regime
Useful for making very sensitive position or force measurements
Gravitational wave detectors
Atomic force microscopes
Explore the quantum-classical boundary on all size scales
Ground state cooling
Direct observation of quantum effects
Superpositions
Entanglement
Decoherence
Tools for quantum information systems

5. 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 fluctuations Zero-point fluctuations remain
One measure of quantumness is the thermal occupation number
Want N  1
Colder oscillator
Stiffer oscillator

6. Reaching the quantum limit in macroscopic mechanical oscillators
Large inertia requires working at lower frequency (Wosc  1/√Mosc)
To reach N = 1
Small m-oscillator  Wosc = 10 MHz and T = 0.5 mK
Large object  Wosc = 1 kHz and T = 50 nK
1010 below room temperature !

7. TRAPPING COOLING 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

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

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

10. A whole host of tricks for atoms and ions (or a few million of them)
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

11. 1997 Nobel Prize in Physics
Steven Chu, Claude Cohen-Tannoudji and William D. Phillips for their developments of methods to cool and trap atoms with laser light
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.

12. What about larger objects? Optical trapping of mirrors

13. Cavity length or laser wavelength
Optical cavities
Light storage device
Two mirrors facing each other
Interference  standing wave
Intracavity power
Cavity length or laser wavelength

14. How to make an optical spring? Radiation pressure force
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

15. 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

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

17. Experimental cavity setup
10%
90%
5 W
Optical fibers
1 gram mirror
Coil/magnet pairs
for actuation (x5)‏

18. Experimental Platform
Seismically isolated optical table
Vacuum chamber
10 W, frequency and
intensity stabilized laser
External vibration isolation

20. Extreme optical stiffness
5 kHz K = 2 x 106 N/m Cavity optical mode  diamond rod
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
Displacement / Force
Phase increases  unstable
Frequency (Hz)

21. Supercold mirrors Toward observing mirror quantum states

22. 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, (2007)

23. Optical spring with active feedback cooling
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
Teff = 6.9 mK N = 105
Mechanical Q = 20000
Cooling factor larger than mechanical Q because Gamma = Omega_eff/Q. The OS increases Omega but doesn’t affect Gamma (OS is non-mechanical), so Q must increase to keep Gamma constant.
T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett 99, (2007)

24. Some other cool oscillators
Toroidal microcavity  g
NEMS  g
AFM cantilevers  10-8 g
Micromirrors  10-7 g
SiN3 membrane  10-8 g
NEMs capacitively coupled to SET (Schwab group, Maryland (now Cornell)
Kippenberg group (Munich)
Harris group (Yale)
Bouwmeester group (UCSB)
Aspelmeyer group (Vienna)
LIGO-MIT group
LIGO
LIGO  103 g
Minimirror  1 g

25. In the (near?) future: Observable quantum effects

26. 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
Quantum state of the gram-scale mirror
Generation of squeezed states of light
Entanglement of light and mirror quantum states
Classical light-oscillator coupling effects en route
Optical cooling and trapping
Light is stiffer than diamond

27. Quantum states of light
Classical light

28. Quantum states of light
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 uncertainty X1 X2

29. 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) X1 X2
Laser X1 X2
Arbitrarily below shot noise
Shot noise limited  (number of photons)1/2 X1 X2 X1 X2
Squeezed vacuum
Vacuum fluctuations

30. How to squeeze photon states?
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

31. Radiation pressure: Another way to squeeze light
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

32. Radiation pressure: Another way to squeeze light
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

33. A radiation pressure dominated interferometer
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

34. Squeezing Squeezing 7 dB or 2.25x
T. Corbitt, Y. Chen, F. Khalili, D.Ottaway, S.Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev A 73, (2006)

35. Closing remarks

36. 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)

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

38. 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

39. And now for the most important part…

40. Cast of characters MIT Collaborators
Timothy Bodiya
Thomas Corbitt
Sheila Dwyer
Keisuke Goda
Nicolas Smith
Christopher Wipf
Eugeniy Mikhailov
Edith Innerhofer
David Ottaway
Sarah Ackley
Jason Pelc
MIT LIGO Lab
Collaborators
Yanbei Chen
Caltech MQM group
Stan Whitcomb
Daniel Sigg
Rolf Bork
Alex Ivanov
Jay Heefner
Caltech 40m Lab
Kirk McKenzie
David McClelland
Ping Koy Lam
Helge Müller-Ebhardt
Henning Rehbein

41. Thanks to… Our colleagues at Funding from LIGO Laboratory
The LIGO Scientific Collaboration
Funding from
Sloan Foundation
MIT
National Science Foundation

42. The End