1. “Traditional” treatment of quantum noise
Shot Noise
Uncertainty in number of photons detected a
(Tunable) interferometer response  Tifo depends on light storage time of GW signal in the interferometer
Radiation Pressure Noise
Photons impart momentum to cavity mirrors Fluctuations in the number of photons a
Shot noise and radiation pressure noise uncorrelated  optimal Pbs for a given Tifo
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

2. The quantum calculation DC strain sensitivity
Buonanno and Chen (PRD 2001)
In signal tuned interferometer shot noise and radiation pressure (back action) noise are correlated
Optical field (which was carrying mirror displacement information) returns to the arm cavity  radiation pressure force depends on test mass motion
Quantized quadrature fields (quantum treatment not necessary when input at SRM is vacuum, can use classical amplitude/phase fluctuations)
Use commutation relations for creation and annhilation operators, correlated two-photon modes

3. Homodyne (DC) readout z0 = homodyne phase
k = coupling constant (ISQL, I0, W, g)
F, f = GW sideband, carrier phase gain in SR cavity
= GW sideband phase gain in arm cavity
r, t = SRM reflection, transmission coefficient
Cij, M, D1,2 = f(r, f, F, k, b)

4. Heterodyne (RF) readout
fD = RF demodulation phase
D+,- = (complex) amplitude of upper, lower RF sideband

5. Preliminary result (not yet correct?)
h(f) (1/rtHz)
frequency (Hz)

6. No crossings  no frequency dependent optimal demod phase
frequency (Hz)
h(f) (1/rtHz)