1. Optical Cooling and Trapping of Macro-scale Objects
Stiffer than diamond
6.9 mK
Stable Optical Spring
Nergis Mavalvala, MIT

2. 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.

3. 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

4. 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

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

6. 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

7. 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

8. 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.

9. 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
2004
Bulk refrigeration – difficult to impossible
Need nonequilibrium cooling techniques similar to laser cooling of atoms, neutral ions.

10. The optical spring effect

11. How to make an optical spring?
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

12. Optical springs and damping
Restoring
Damping
Anti-damping
Anti-restoring
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
Cavity cooling
Blue shift (higher f) optical spring
Red shift (lower f)  cavity cooling

13. Stable optical springs
Optical springs are always unstable if optical forces dominate over mechanical ones
Stabilized by electronic feedback in the past
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

14. An all optical trap for gram-scale mirrors

15. Phase II cavity
10%
90%
5 W

17. Mechanical oscillator
Optical fibers
1 gram mirror
Coil/magnet pairs
for actuation(x5)‏

18. 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)

19. Trapped and cooled

20. 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)

21. Optical spring with active feedback cooling for 1 gram mirror
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)

22. Cooling the kilogram scale mirrors of Initial LIGO
Teff = 1.4 mK N = 234 T0/Teff = 2 x 108
Mr ~ 2.7 kg ~ 1026 atoms
Wosc = 2 p x 0.7 Hz
LIGO Scientific Collaboration

23. 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

24. Cavity cooling
200x
1012x

25. Future prospects for MIT experiment

26. 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

27. Approaching a quantum state
MIT experiment with 1 gram mirrors and two cavities
Without optical trapping
With optical trap at 1 kHz
Hbar/kB = 1.05e-34/1.38e-23 = 7.6e-12

28. Present status Factor of 10 between present noise floor and target
Blue curve = noise with 50 mW of input power and detuning = 1
Red line = noise level required to observe sqz and quant. rp with 5 W of input power
Factor of 10 between present noise floor and target

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

30. The end