“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

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

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)

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

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

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