Traditional treatment of quantum noise q Shot Noise

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“Traditional” treatment of quantum noise q. Shot Noise § Uncertainty in number of photons

“Traditional” treatment of quantum noise q. Shot Noise § Uncertainty in number of photons detected a § (Tunable) interferometer response Tifo depends on light storage time of GW signal in the interferometer q. 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 1

The quantum calculation DC strain sensitivity q. Buonanno and Chen (PRD 2001) § In

The quantum calculation DC strain sensitivity q. 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 2

Homodyne (DC) readout z 0 = homodyne phase k = coupling constant (ISQL, I

Homodyne (DC) readout z 0 = homodyne phase k = coupling constant (ISQL, I 0, W, g) F, f = GW sideband, carrier phase gain in SR cavity b = GW sideband phase gain in arm cavity r, t = SRM reflection, transmission coefficient Cij, M, D 1, 2 = f(r, f, F, k, b) 3

Heterodyne (RF) readout f. D = RF demodulation phase D+, - = (complex) amplitude

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

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

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

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

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