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“Traditional” treatment of quantum noise

“Traditional” treatment of quantum noise. Shot Noise Uncertainty in number of photons detected a (Tunable) interferometer response  T ifo depends on light storage time of GW signal in the interferometer Radiation Pressure Noise

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“Traditional” treatment of quantum noise

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  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 mirrorsFluctuations in the number of photons a Shot noise and radiation pressure noise uncorrelated  optimal Pbs for a given Tifo

  2. The quantum calculationDC 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. h(f) (1/rtHz) frequency (Hz) Preliminary result (not yet correct?)

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

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