1. TeV Particle Astrophysics August 2006 Caltech Australian National University Universitat Hannover/AEI LIGO Scientific Collaboration MIT Corbitt, Goda, Innerhofer, Mikhailov, Ottaway, Wipf Path to Sub-Quantum-Noise-Limited Gravitational-wave Interferometry

2. Outline  The quantum noise limit in GW ifos  Sub-quantum noise limited ifos  Injecting squeezed vacuum  Setting requirements – the wishlist  Generating squeezed states  Nonlinear optical media – “crystal”  Radiation pressure coupling – “ponderomotive”  Recent progress and present status

3. Optical Noise  Shot Noise  Uncertainty in number of photons detected   Higher circulating power P bs  low optical losses  Frequency dependence  light (GW signal) storage time in the interferometer  Radiation Pressure Noise  Photons impart momentum to cavity mirrors Fluctuations in number of photons   Lower power, P bs  Frequency dependence  response of mass to forces  Optimal input power depends on frequency

4. Initial LIGO Input laser power ~ 6 W Circulating power ~ 20 kW Mirror mass 10 kg

5. A Quantum Limited Interferometer LIGO I Ad LIGO Seismic Suspension thermal Test mass thermal Quantum Input laser power > 100 W Circulating power > 0.5 MW Mirror mass 40 kg

6. Some quantum states of light  Heisenberg Uncertainty Principle for EM field  Phasor diagram analogy  Stick  dc term  Ball  fluctuations  Common states  Coherent state  Vacuum state  Amplitude squeezed state  Phase squeezed state McKenzie Associated with amplitude and phase

7. Squeezed input vacuum state in Michelson Interferometer X+X+ XX X+X+ XX X+X+ XX X+X+ XX  Consider GW signal in the phase quadrature  Not true for all interferometer configurations  Detuned signal recycled interferometer  GW signal in both quadratures  Orient squeezed state to reduce noise in phase quadrature Laser

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

9. Squeezed vacuum states for GW detectors  Requirements  Squeezing at low frequencies (within GW band)  Frequency-dependent squeeze angle  Increased levels of squeezing  Long-term stable operation  Generation methods  Non-linear optical media (  (2) and  (3) non-linearites)  crystal-based squeezing  Radiation pressure effects in interferometers  ponderomotive squeezing

10. How to make a squeezed state?  Correlate the ‘amplitude’ and ‘phase’ quadratures  Correlations  noise reduction  How to correlate quadratures?  Make noise in each quadrature not independent of the other  (Nonlinear) coupling process needed  For example, an intensity-dependent refractive index couples amplitude and phase  Squeezed states of light and vacuum

11. Squeezing using nonlinear optical media

12. Optical Parametric Oscillator SHG

13. Squeezed Vacuum

14. Low frequency squeezing at ANU ANU group  quant-ph/0405137 McKenzie et al., PRL 93, 161105 (2004)

15. Injection in a power recycled Michelson interferometer K.McKenzie et al. Phys. Rev. Lett., 88 231102 (2002)

16. Injection in a signal recycled interferometer Vahlbruch et al. Phys. Rev. Lett., 95 211102 (2005)

17. Squeezing using radiation pressure coupling

18. The principle  Use radiation pressure as the squeezing mechanism  Consider an optical cavity with high stored power and a phase sensitive readout  Intensity fluctuations (radiation pressure) drive the motion of the cavity mirrors  Mirror motion is then imprinted onto the phase of the light  Analogy with nonlinear optical media  Intensity-dependent refractive index changes couple amplitude and phase

19. The “ponderomotive” interferometer Key ingredients  Low mass, low noise mechanical oscillator mirror – 1 gm with 1 Hz resonant frequency  High circulating power – 10 kW  High finesse cavities 15000  Differential measurement – common-mode rejection to cancel classical noise  Optical spring – noise suppression and frequency independent squeezing

20. Noise budget

21. Noise suppression Displacement / Force 5 kHz  K = 2 x 10 6 N/m Cavity optical mode  diamond rod Frequency (Hz)

22. 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 the most promising approach  Crystal squeezing mature  3 to 4 dB available in f>100 Hz band  Ponderomotive squeezing getting closer  Factors of 2 to 5 improvements foreseeable in the next decade  Not fundamental but technical  Need to push on this to be ready for future instruments

23. The End