1. Squeezed Input Interferometer
Laser
GW Detector
Faraday isolator
The squeeze source drawn is a ponderomotive squeezer, but it could be any other squeeze source, e.g. an optical parametric oscillator, like the one shown in last slide.
Squeeze
Source
Homodyne Detector
GW Signal

2. Radiation-oscillator coupling  Amplitude-phase correlations
1. Light with amplitude fluctuations DA
incident on mirror
Movable mirror
Field transformation:
Incident laser light is in a coherent state (noise ball)
Coupling to mirror motion
Reflected light is in a squeezed state (noise ellipse)
2. Radiation pressure due to DA causes mirror to move by Dx
3. Phase of reflected light Df depends on mirror position and hence light amplitude, i.e DA  Dx  Df

3. Nonlinear optical mediumb b a a
Parametric oscillation
Second harmonic generation
The black cloud is a nonlinear material, e.g. LiNbO3.
Operators a and b are creation and annihilation operators
a  low energy photon (red, 1064 nm)
b  high energy photon (green, 532 nm)
First term in Hamiltonian gives optical parametric oscillation (OPO)  One high energy photon gives two (correlated) low energy photons
Second term in Hamiltonian gives SHG  two low energy photons give on high energy photon
Energy and momentum are conserved. a a
The output photon quadratures are correlated a b a
Parametric amplification

4. Optical Parametric Oscillator
SHG