1. Advanced Optical Sensing
Path to Sub-Quantum-Noise-Limited Gravitational-wave Interferometry
MIT Corbitt, Goda, Innerhofer, Mikhailov, Ottaway, Wipf
Caltech
Australian National University
Universitat Hannover
TeV Particle Astrophysics August 2006

2. Quantum noise limits in GW ifos Sub-quantum noise limited ifos
Outline
Quantum noise limits 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. Radiation Pressure Noise
Optical Noise
Shot Noise
Uncertainty in number of photons detected a
Higher circulating power Pbs a low optical losses
Frequency dependence a light (GW signal) storage time in the interferometer
Radiation Pressure Noise
Photons impart momentum to cavity mirrors Fluctuations in number of photons a
Lower power, Pbs
Frequency dependence a response of mass to forces
Shot noise:
Laser light is Poisson distributed  sigma_N = sqrt(N)
dE dt >= hbar  d(N hbar omega) >= hbar  dN dphi >= 1
Radiation Pressure noise:
Pressure fluctuations are anti-correlated between cavities
 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
Associated with amplitude and phase
McKenzie

7. Squeezed input vacuum state in Michelson Interferometer
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 X+ X- X+ X- X+ X- X+ X-

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

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 (c(2) and c(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

13. Squeezed Vacuum

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

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

16. Injection in a signal recycled interferometer
Vahlbruch et al. Phys. Rev. Lett., (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
5 kHz K = 2 x 106 N/m Cavity optical mode  diamond rod
Displacement / Force
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