1. Quantum effects in Gravitational-wave Interferometers
Nergis Mavalvala LIGO Laboratory Quantum Measurement Group September 2004

2. Quantum Noise in Optical Measurements
Measurement process
Interaction of light with test mass
Counting signal photons with a photodetector
Noise in measurement process
Poissonian statistics of force on test mass due to photons  radiation pressure noise (RPN) (amplitude fluctuations)
Poissonian statistics of counting the photons  shot noise (SN) (phase fluctuations)

3. Limiting Noise Sources: 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

5. Advanced LIGO A Quantum Limited Interferometer
LIGO I
Ad LIGO
Seismic
Suspension thermal
Test mass thermal
Quantum

6. Sub-Quantum Interferometers Generation 2

7. Some quantum states of light
Analogous to the phasor diagram
Stick  dc term
Ball  fluctuations
Common states
Coherent state
Vacuum state
Amplitude squeezed state
Phase squeezed state
McKenzie

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

9. Back Action Produces Squeezingf
Squeezing produced by back-action force of fluctuating radiation pressure on mirrors
b a
Vacuum state enters anti-symmetric port
Amplitude fluctuations of input state drive mirror position
Mirror motion imposes those amplitude fluctuations onto phase of output field a1 a2
“In” mode at omega_0 +/- Omega  |in> = exp(+/- 2*j* beta) S(r, phi) |out>
Heisenberg Picture: state does not evolve, only operators do. So |out> vacuum state is squeezed by factor sinh(r) = kappa/2 and angle phi = 0.5 arcot(kappa/2).
Spectral densities assuming input vacuum state:
S_b1 = exp(-2 r) ~ 1/kappa when kappa >> 1
S_b2 = exp(+2 r) ~ kappa
S_{b1 b2} = 0

10. Sub-quantum-limited Advanced LIGOX+ X-
Quantum correlations (Buonanno and Chen)
Input squeezing

11. Squeezed state generation with nonlinear optical media

12. Vacuum seeded OPO
ANU group  quant-ph/

13. Key ingredients Media with high nonlinearity
Quadrature-sensitive locking techniques
Optically pure states
Low losses

14. Squeezing using back-action effects

15. “Ponderomotive” Experiment
A “tabletop” interferometer to generate squeezed light
Use radiation pressure as the squeezing mechanism
Alternative to crystal-based squeezing
Test quantum-limited radiation pressure effects
Gain confidence that the modeling is correct
Expected noise sources do not prohibit squeezing
Test noise cancellations via Michelson detuning
Useful for all interferometers
Squeezing produced even when the sensitivity is far worse than the Standard Quantum Limit
Due to the optical spring
Study intrinsic quantum physics of optical field --mechanical oscillator correlations

16. High circulating laser power High-finesse cavities
Key ingredients
High circulating laser power
10 kW
High-finesse cavities
25000
Light, low-noise mechanical oscillator mirror
1 gm with 1 Hz resonant frequency
Optical spring
Detuned arm cavities

17. Ponderomotive squeezing

18. Noise budget