1. The Quantum Limit and Beyond in Gravitational Wave Detectors
Quantum nature of light
Quantum states of mirrors
Nergis Mavalvala APS, April 2009

2. Outline Quantum limit for gravitational wave detectors
Origins of the quantum limit
Vacuum fluctuations of the EM field
Quantum states of light
Squeezed state injection and generation
Quantum states of the mirrors
Radiation pressure induced dynamics
Prospects for observing quantum effects in macroscopic objects (mirrors)

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

4. Advanced LIGO Quantum noise everywhere
Radiation pressure noise
Stronger measurement  larger backaction
Shot noise
More laser power  stronger measurement

5. Origin of the Quantum Noise Vacuum fluctuations

6. 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

7. 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)
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

8. 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

9. Advanced LIGO with squeeze injection
Radiation pressure
Shot noise

10. Desired properties of squeezed states for GW detectors
Squeezing in the GW band (10 Hz to 10 kHz)
Large squeezing factors (e.g. 10 dB  factor of 3 improvement in strain sensitivity)
Compatibility with other noise sources (“Do no harm” in GW band)
Stable long term operation of squeezer
Frequency-dependent squeezing

11. Squeezed state generation

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

13. 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

14. Squeezing with optical nonlinearity
The sum of correlated upper and lower quantum sidebands  a squeezed state

15. Squeezing using nonlinear optical media

16. Basic principle The output photon quadratures are correlated a a b b a
Parametric oscillation
Second harmonic generation a a
The output photon quadratures are correlated a b a
Parametric amplification

17. Typical squeezer apparatus
Noise power (dBm/rtHz)
Frequency (Hz)
Vahlbruch et al., New Journal of Physics 9, 371 (2007)
Vacuum (shot)
Squeezed
Dark
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

18. Squeezing injection Second harmonic generator (SHG) Laser
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

19. Frequency-dependent Second harmonic generator (SHG) Laser
Noise power (dBm)
Frequency (MHz)
Vahlbruch et al., Phys.Rev.Lett.95, (2005)
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
OPA
Faraday rotator
ASPD
Filter cavities
SHG

20. 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

21. Squeeze injection in a suspended-mirror interferometer: 40m prototye (Caltech)
Here is the apparatus of the quantum enhanced detector. Just like the LIGO detector, the interferometer has a Fabry-Perot cavity in each arm, a so-called power-recycling mirror, and a signal-recycling mirror. And there is a laser frequency- and intensity-stabilizer to stabilize the laser. Also, there is a triangular cavity with 4kHz linewidth to further suppress the laser intensity and frequency noise. Finally, I built the squeezer and injected the squeezed state into the output port of the interferometer. The squeezer is mainly composed of an optical parametric oscillator and a second harmonic generator.
I will explain a little bit more about each major component.

22. Measurement of squeezing Balanced Homodyne Detection
SQZ LO

23. Quantum enhancement at 40m
2.9 dB or 1.4x
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)

24. Crystal squeezing experiments Progress in last ~half decade
Squeezing at audio frequencies
Filter cavities for frequency-dependent squeezing
Detailed calculations of noise couplings to establish fundamental limits
Coherently controlled squeezing  long term operation
10 dB of available squeezing
GW interferometers
6 dB at frequencies > 10 Hz, 11 dB at MHz
Suspended interferometer test at 40m

25. Squeezing Enhancement in LIGO
Design squeezing source for injection into Advanced LIGO
Possible test of low-noise, low-frequency performance in Enhanced LIGO

26. Squeezing Enhancement in GEOHF
Improve high frequency sensitivity
Expect to install in summer 2009

27. Radiation pressure the other quantum noise

28. Radiation pressure rules!
Experiments in which radiation pressure forces dominate over mechanical forces
Classical light-oscillator coupling effects (dynamical backaction)
Optical cooling and trapping of mirrors
Opportunity to study quantum effects in macroscopic systems
Observation of quantum radiation pressure
Generation of squeezed states of light
Entanglement of mirror and light quantum states
Quantum ground state of (kilo)gram-scale mirrors
Optical spring
Optical damping

29. Optically trapped and cooled mirror
Optical fibers
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.
1 gram mirror
T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett 99, (2007)

30. Cast of characters MIT NSF Collaborators Keisuke Goda Thomas Corbitt
Christopher Wipf
Timothy Bodiya
Sheila Dwyer
Nicolas Smith
Eugeniy Mikhailov
Edith Innerhofer
MIT LIGO Lab
NSF
Collaborators
Roman Schnabel and group
Henning Vahlbruch
Yanbei Chen and group
Helge Müller-Ebhardt
Henning Rehbein
Stan Whitcomb
Daniel Sigg
Rolf Bork
Alex Ivanov
Jay Heefner
Caltech 40m Lab
David McClelland and group
Kirk McKenzie
Ping Koy Lam
LIGO Scientific Collaboration

31. The End GW Detector Laser Faraday isolator Homodyne Detector GW Signal
SHG
Faraday isolator
OPO
Homodyne Detector
Squeeze
Source
GW Signal

32. Supplementary info

33. Quantum states of light
Classical light
Quantum optics

34. Squeezing with optical nonlinearity
The sum of correlated upper and lower quantum sidebands  a squeezed state

35. High Level of Squeezing & Long-Term Stability
High nonlinearity
LiNbO3 vs PPKTP
Low optical losses
Use supermirrors
High pump power
1 W or higher
Thermally stable
Wider phase-matching temperature range
PPKTP (KTiOPO4) Crystal

36. Second-Harmonic Generator (SHG)
SHG conversion efficiency = 30%
The second-harmonic field pumps the OPO cavity

37. Optical Parametric Oscillator (OPO)
High power (few 100 mW) green pump field in OPO correlates upper and lower quantum sidebands around carrier  squeezing
Output Coupler
The OPO is a 2.2cm long cavity with a quasi-phase matched periodically poled KTP crystal with two external mirrors in a traveling wave cavity configuration. The vacuum-seeded OPO is pumped by an energetic second-harmonic field to correlate upper and lower quantum sidebands around the carrier frequency and generates a squeezed state of vacuum.
Input Coupler
PPKTP Crystal

38. Measurement Balanced Homodyne Detection
SQZ LO

39. Audio frequency squeezing
Noise power (dBm/rtHz)
Frequency (Hz)
Vahlbruch et al. (2007)
Vacuum (shot)
Squeezed
Dark

40. Frequency dependent squeezing
Vahlbruch et al., Phys.Rev.Lett.95, (2005)

41. Frequency-dependent squeezing
Noise power (dBm)
Frequency (MHz)
Vahlbruch et al., Phys.Rev.Lett.95, (2005)

42. Frequency-dependence with state tomography

43. Frequency-dependence with state tomography