1. Squeezed states in GW interferometers
NSF review November 2005

2. Why should we squeeze? To improve the shot noise limit More power
Increase power
Reduce quadrature vacuum noise  squeeze
Reduction in shot noise by squeezing can allow for reduction in circulating power (for the same sensitivity) – important for power-handling
More power
Radiation pressure (dominates at low freqs)
Instabilities
Thermal effects due to absorption
Photodetection, power handling
Squeezing ...

3. Sub-quantum-limited interferometer
Narrowband
Broadband
Broadband Squeezed X+ X-
Quantum correlations
Input squeezing

4. Squeezed vacuum Requirements Generation methods Challenges
Squeezing at low frequencies (within GW band)
Frequency-dependent squeeze angle
Increased levels of squeezing
Generation methods
Non-linear optical media (c(2) and c(3) non-linearites)  crystal-based squeezing
Radiation pressure effects in interferometers  ponderomotive squeezing
Challenges
Frequency-dependence  filter cavities
Amplitude filters
Squeeze angle rotation filters
Low-loss optical systems

5. Present status Nonlinear optical media
Low frequency squeezing demonstrated at ANU (300 Hz) and MIT (4 kHz)
“Noise locking” demonstrated
No coherent amplitude for locking in case of vacuum state
Frequency dependent squeezing demonstrated at few MHz (Hannover)
Full interferometer test being devised (40m)

6. Radiation pressure effects
Experiment design complete
Experiment phase 1 complete
Single cavity with 250g mirrors, 1000 finesse
Optical spring established and stabilized
Parametric instability measured and controlled
Full interferometer in summer 2006

7. QND techniques needed to do better
Conclusions
Advanced LIGO is expected to reach the quantum noise limit in most of the band
QND techniques needed to do better
Squeezed states of the EM field appears to be a promising approach
Factors of 2 to 5 improvements foreseeable in the next few years
Not fundamental but technical
Need to push on this to be ready for third generation instruments

8. The End

9. What is a squeezed state?
Heisenberg  minimum uncertainty
Equal uncertainty in both quadratures
Squeezing  reduce uncertainty in one quadrature at the expense of increased uncertainty in orthogonal quadrature
Area in quadrature phase space conserved
Uncertainty circle  ellipse
How to squeeze?
Correlate quadratures
Why is it useful
Line up signal phasor with narrowest part of ellipse
Noise in measurement of that signal lower than the quantum noise limit

10. Squeezing using nonlinear optical media

11. Nonlinear optical media
Vacuum seeded OPO
ANU group  quant-ph/

12. Squeezing using back-action effects

13. The principle
A “tabletop” interferometer to generate squeezed light as an alternative to nonlinear optical media
Use radiation pressure as the squeezing mechanism
Relies on intrinsic quantum physics of optical field-mechanical oscillator correlations
Squeezing produced even when the sensitivity is far worse than the SQL
Due to noise suppression a la optical springs

14. The Ponderomotive Interferometer

15. High circulating laser power High-finesse cavities
Key ingredients
High circulating laser power
10 kW
High-finesse cavities
15000
Light, low-noise mechanical oscillator mirror
1 gm with 1 Hz resonant frequency
Optical spring
Detuned arm cavities

16. Noise budget

17. Noise budget – Equivalent displacement