1. Interferometric Gravitational Wave Detectors: Giant Quantum Machines
Nergis Mavalvala
Department of Physics
Massachusetts Institute of Technology
Pracqsys 2010, June 2010

2. Outline Gravitational waves Interferometric detectors
Next generation detectors and the quantum limit
Getting past the quantum limit
Experiments
Quantum optics
Quantum optomechanics
Necessary building blocks in the classical regime
Progress toward the quantum regime

3. Gravitational waves (GWs)
Prediction of Einstein’s General Relativity (1916)
Indirect detection led to Nobel prize in 1993
Ripples of the space-time fabric
GWs stretch and squeeze the space transverse to direction of propagation
Emitted by accelerating massive objects
Cosmic explosions
Compact stars orbiting each other
Stars gobbling up stars
“Mountains” on stellar crusts 

4. GW detector at a glance Mirrors hang as pendulums Quasi-free particles
Respond to passing GW
Filter external force noise
4 km
20 kW
Optical cavities
Mirrors facing each other
Builds up light power
Lots of laser power P
Signal  P
Noise 
10 W

5. Global network of detectors
GEO
VIRGO
LIGO
TAMA
AIGO
LIGO
LISA

6. Quantum noise in Initial LIGO
Shot noise
Photon counting statistics
Radiation pressure noise
Fluctuating photon number exerts a fluctuating force

7. LIGO listened… And had something to say

8. The search for GRB070201 GRB 070201 Looked for a GW signal in LIGO
Very luminous short duration, hard gamma-ray burst
Detected by Swift, Integral, others
Consistent with being in M31
Leading model for short GRBs: binary merger involving a neutron star
Looked for a GW signal in LIGO
No plausible GW signal found
Can say with >99% confidence that GRB was NOT caused by a compact binary star merger in M31
Conclusion: it was most likely a Soft Gamma Repeater giant flare in M31
25%
50%
75%
90%
DM31
This is the improved position localization, using Konus-Wind, INTEGRAL and MESSENGER
Leading model for short hard GRBs: binary merger involving a neutron star (found in giant elliptical galaxies, too old (> 5 Gyr to be supernovae). SHBs in non-star-forming region or gaint ellipticals which contain large population of LMXBs that accrete and merge. Core collapse in young, star forming regions.
SGR: Crustal cracking may excite quasinormal modes which emit GW.
Significance of extragalactic soft gamma repeater (SGR) giant flares as origin of some short hard GRBs
The LIGO result is mentioned in these papers as evidence against a merger
Ofek et al.: “Given the properties of this GRB, along with the fact that LIGO data argue against a compact
binary merger origin in M31, it is an excellent candidate to have been an extragalactic SGR giant flare…. However, we cannot rule out the possibility that it was a short-duration GRB in the background.”
Mazets et al.: Title of paper (paraphrased) is: “A giant flare from an SGR in M31”
Abbott et al., Ap. J 681, 1419 (2008)
Mazets et al., Ap. J 680, 545 (2008)
Ofek et al., Ap. J 681, 1464 (2008)

9. Farther away

10. More laser power  stronger measurement Radiation pressure noise
Strain sensitivity
Shot noise
More laser power  stronger measurement
Radiation pressure noise
Stronger measurement  larger backaction

11. Origin of the Quantum Noise Vacuum fluctuations

12. 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)
Goda et al., Nature Physics (2008)
Radiation pressure noise
Quantum fluctuations exert fluctuating force  mirror displacement X1 X2
Laser X1 X2
Shot noise limited  (number of photons)1/2
Arbitrarily below shot noise X1 X2 X1 X2
Vacuum fluctuations
Squeezed vacuum

13. Quantum Enhancement Squeezed state injection

14. Squeezing injection in Advanced LIGO
Laser
GW Detector
SHG
Faraday isolator
Squeezing
source
The squeeze source drawn is an OPO squeezer, but it could be any other squeeze source, e.g. ponderomotive squeezer.
OPO
Homodyne Detector
Squeeze
Source
GW Signal

15. Advanced LIGO with squeeze injection
Radiation pressure
Shot noise

16. Squeezed State Generation

17. How to squeeze?
My favorite way
A tight hug

18. 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

19. Typical squeezer apparatus
Second harmonic generator (SHG)
Convert 1064 nm  532 nm with ~50% efficiency
Optical parametric oscillator (OPO)
Few 100 mW pump field (532 nm) correlates upper and lower quantum sidebands around carrier (1064 nm)  squeezing
Balanced homodyne detector
Beat local oscillator at 1064nm with squeezed field
Laser
IFO
OPO
Faraday rotator
ASPD
SHG

20. Squeezing in GW (audio) band
Vahlbruch et al,. PRL 2008

21. Squeezing injection in 40m prototype
Laser
Prototype GW detector
SHG
Faraday isolator
The squeeze source drawn is an OPO squeezer, but it could be any other squeeze source, e.g. ponderomotive squeezer.
OPO
Homodyne Detector
Squeeze
Source
Diff. mode signal

22. Squeezing injection in a prototype interferometer
K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K.McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, Nature Physics 4, 472 (2008)
2.9 dB or 1.4x

23. Squeezed state injection has arrived!
Implementation in GEO600
Installed, commissioning phase
Implementation in a 4km LIGO detector
Under construction, installation and commissioning begin 4Q 2010
A direct application of quantum metrology

24. Radiation pressure
The other side of the quantum optical coin

25. 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 ground state of the gram-scale mirror
Entanglement of mirror and light quantum states
Classical light-oscillator coupling effects en route (dynamical backaction)
Optical cooling and trapping
Light is stiffer than diamond

26. 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

27. 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
Fluctuation-dissipation theorem
Connect a high Q, low stiffness mechanical oscillator to a stiff optical spring  DILUTION
Dilution – a fraction of the energy of the oscillator is stored in the optical field instead of in the elastic flexing of the wire, or in the acoustic modes
The optical spring shifts the oscillator's resonant frequency while leaving its mechanical losses unchanged. The mechanical quality factor $Q_M$, as limited by those losses, is increased by the factor $\Omega_{\rmeff} / \Omega_M$, where $\Omega_M$ is the natural frequency of the free mechanical oscillator.
We refer to this as ``optical dilution'', analogous to the phenomenon of ``damping dilution'' that accounts for the fact that the $Q$ of the pendulum mode can be much higher than the mechanical $Q$ of the material of which it is made~\cite{saulsonPRD1990,dilution}.
This mitigation of intrinsic thermal noise is possible because a fraction of the energy is stored in the (noiseless) gravitational field. In the case of the pendulum, the dilution factor depends on the amount of elastic energy stored in the flexing wire compared to the energy stored in the gravitational field -- approximated by the ratio of the gravitational spring constant to the mechanical spring constant.
Optical dilution accounts for the fact that thermal noise in our mechanical oscillator is reduced due to energy stored in the optical field (the optical spring force acts similar to the gravitational force).
True for any non-mechanical force ( non-dissipative or “cold” force ), e.g. gravitation, electronic, magnetic

28. The optical spring effect and optical trapping of mirrors

29. Optical springs and damping
Restoring
Damping
Anti-damping
Anti-restoring
Radiation pressure of light in an optical cavity  force on mirror
Detune a resonant cavity to higher frequency (blueshift)
Real component of optical force  restoring
But imaginary component (cavity time delay)  anti-damping
Unstable
Can stabilize with feedback
Cavity cooling
Optical spring
Blue shift (flaser > fcavity) optical spring
Red shift (flaser < fcavity)  cavity cooling

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

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

32. 10 W, frequency and
intensity stabilized laser
External vibration isolation

33. Trapping and cooling Dynamic backaction cooling
Stable optical trap with two colors
Stiff!
Stable!
T. Corbitt et al., Phys. Rev. Lett 98, (2007)

34. Active feedback cooling
Measure mirror displacement
Filter displacement signal
Feed it back to mirror as a force
Controller
PDH
Laser
Continuous measurement  measurement-induced decoherence
EOM
PBS
QWP
Continuous measurement  measurement-induced decoherence

35. 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)

36. Quantum measurement in gravitational wave detectors

37. Even bigger, even cooler
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
SQL

38. Active feedback cooling + spring
Measure mirror displacement
Filter displacement signal
Feed it back to mirror as a force
Controller
PDH
Laser
EOM
PBS
QWP

39. 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

40. Closing remarks

41. 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)

42. Quantum radiation pressure effects
Squeezing
Present status
Squeezed vacuum generation

43. LIGO Quantumness
N = 234
SQL
N = 1

44. And now for the most important part…

45. Cast of characters MIT Collaborators Thomas Corbitt Christopher Wipf
Timothy Bodiya
Sheila Dwyer
Nicolas Smith
Eric Oelker
MIT LIGO Lab
Collaborators
Yanbei Chen and group
Stan Whitcomb
Daniel Sigg
Rolf Bork
Alex Ivanov
Jay Heefner
LIGO Scientific Collaboration

46. The End Gravitational wave detectors Quantum nature of light
Quantum states of mirrors